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User talk:Cumguzzler

Hello there, welcome to the 'pedia! Nice work on taking out all those "virulents" - that adjective is not something we want used a lot around here. I also liked your work on World Church of the Creator. However, there is a problem and I must admit I and several others are guilty of being lazy: We haven't yet made a warning for new users about our user name policy. In short we do not allow for offensive user names. The developers will therefore be renaming your account but we need to know which user nic you want. You can respond here. Cheers! --maveric149

 * it has now: see no offensive usernames

Seeing you have missed the message above, I'm just adding something so you'll see this in the recent changes page. Welcome, but please change your name to something else! --Robert Merkel 07:26 Jan 16, 2003 (UTC)

 * Hi, there, whoever you are. You've added some good contributions here - how did you determine that the plane in that phony tourist photograph was a 757, by the way? - but I must agree with Robert's thoughts - a change of 'nic' is needed in accordance to common sense and Wikipedia policy.

 * Two questions, just out of curiosity, Mr. Merkel:

 * What makes you think this user is a "Mr."? It seems to me this name swings either way, depending on whether the person is heterosexual, homosexual, and/or autosexual.

 * What makes you think this user hasn't seen the messages on the user and usertalk pages? My guess was the person had seen them and was ignoring them in the reasonable expectation that the community would talk the issue to death before, if ever, getting around to changing this username. -- isis 07:39 Jan 16, 2003 (UTC)

 * Mr or Ms., makes no difference as far as the name goes, it's still offensive. As to why I referred to the person as "Mr. Guzzler" it was because I feel extremely uncomfortable calling somebody "Cumguzzler" even if that's the name they give themselves, and in my experience on the Net few women, regardless of their sexual preferences, would give themselves such a name, particularly on a website not dedicated to discussion of sexual matters.  It was probably wrong to have made that assumption.  Sorry about that.

 * Secondly, nobody's been complaining about this person's actual edits so far so I (and I presume other regular users) was willing to assume that given a chance to respond reasonably, they would.  I may be wrong, in which case the name will be changed in fairly short order.  --Robert Merkel 08:07 Jan 16, 2003 (UTC)

Guzzler, seeing you're clearly active and reading recent changes, must have seen the messages on your talk page, and have not replied, I expect the developers will assume that you have no opinion on a preferred name change and will just pick a new one arbitrarily. --Robert Merkel 08:45 Jan 16, 2003 (UTC)

I reccomend XXXguzzler Vera Cruz

 * How about "cumquat"? -- isis 08:52 Jan 16, 2003 (UTC)

How about "Joseph" -Sv

or "Mary"-Sv

 * How about "757" - I was impressed by that Flight 11 business. -Arno

Why not simply User:C. Guzzler? --mav

Just e-mail Brion, he's probably the only one who can make the change. --Eloquence 09:23 Jan 16, 2003 (UTC)

I could deal with just plain "Guzzler." Part of an effective process functioning is the responsibility of the participants to be sensitive to the sensibilities of others involved. I think I could safely say that Wikipedians generally tend to be pretty liberal and intelligent, but there's clearly a great deal of discomfort with "Cumguzzler," including on my own part. I have to question what someone is trying to accomplish by parading such intimations of overt sexuality in a public forum in such a manner that they're guaranteed to know that they're offending people. What the hell is the point?

--user:jaknouse

Guzzler you should respond to these messages or your username will be changed without your consent. Mintguy

I wonder is she/he knows actually looks at recent changes. - fonzy

 * It's highly likely that they have, as they have made some further edits to articles that were recently edited (and were thus in the recent changes list) Unless they're clairvoyant, they are following Recent Changes.  --Robert Merkel

I think anyone who makes a name like this does it to get attention, be "in your face" defiantly, and has a mini control drama running intentionally or otherwise. I don't like the name, but I didn't want to be the first person to whine about it. Maybe this person is mixing Latin cum and guzzler. Riiiightt! =) BF

Cumguzzler has changed today to using the names 'Cockgoblin' and now 'Polesmoker'. One might generously assume this to be unilateral de-escalation (using progressively less overt names until one is found that will be tolerated by other users while still making whatever point is intended). --Brion 00:28 Jan 17, 2003 (UTC)

 * Is he there yet? To one "that will be tolerated by other users", I mean.  In any event, Brion, could you please close out his earlier names now and convert the contributor's name for his old edits to his current name, so users can find him and he can get credit for his substantive work? -- isis 00:48 Jan 17, 2003 (UTC)

 * 'E's also made an edit as CrucifiedChrist and is lately back to Cumguzzler. --Brion 01:06 Jan 17, 2003 (UTC)

 * I wondered if that was 'im/'er. A quote is in order. "If it wasn't for your immaturity none of this would've happened.. oooo... this could be messy[sticky]...ooooo but you don't seem to mind." BF

Hi. I changed your username to CG. --Uncle Ed 19:22 Jan 17, 2003 (UTC)

 * One potential problem, people may confuse him with GC. . - Arno.
 * I have once. Maybe TWFKACG?  ;-)  Koyaanis Qatsi

 * So did I. Why not C. Guzzler? It would be a kinda inside joke about what the "C" means. --mav

Your username
Your username has been blocked as inappropriate, in line with our blocking policy. You are encouraged to create a new account and contribute to Wikipedia under a more appropriate username, and in a constructive manner. See Username for guidance on selecting an appropriate username. You may also edit Wikipedia without creating an account. You are not allowed to edit Wikipedia under an inappropriate username. If you would like to discuss the block, you may edit your talk page or email the administrator who blocked you.

Due to Wikipedia's mechanism for enforcing name changes, your IP address may be temporarily blocked. Unless you have also been engaging in vandalism, we will remove that block as soon as possible—if this doesn't happen within an hour or so, please email an administrator and explain the situation (see the list of administrators).

If you want to keep the contributions from your old account for your new one, leave a note on Changing username. This can only be done before you create the new one. — Preceding unsigned comment added by Rhobite (talk • contribs) 21:19, 26 September 2005 (UTC)

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: User talk:Cumguzzler


text:
Girl, Interrupted

Girl, Interrupted is a best-selling 1993 memoir by American author Susanna Kaysen, relating her experiences as a young woman in an American psychiatric hospital in the 1960s after being diagnosed with borderline personality disorder.

The memoir's title is a reference to the Johannes Vermeer painting Girl Interrupted at Her Music. Kaysen draws a parallel between the Vermeer painting and her own life by equating music interrupting the girl, with the struggles of poor mental health in adolescence interrupting healthy development, both serving as an impediment to personal evolution. Kaysen draws on the painting as a source of inspiration for critical analysis of the female teenage experience.

While writing the novel Far Afield, Kaysen began to recall her almost two years at McLean Hospital. She obtained her file from the hospital with the help of a lawyer.

A film adaptation of the memoir directed by James Mangold, and starring Winona Ryder and Angelina Jolie, was released in 1999.

Plot
In April 1967, 18-year-old Susanna Kaysen is admitted to McLean Hospital, in Belmont, Massachusetts, after attempting suicide by overdosing on pills. She denies that it was a suicide attempt to a psychiatrist, who suggests she take time to regroup in McLean, a private mental hospital. Susanna is diagnosed with borderline personality disorder, and her stay extends to 18 months, rather than the proposed couple of weeks.

Fellow patients Polly, Cynthia, Lisa Rowe, Lisa Cody, Georgina and Daisy contribute to Susanna's experiences at McLean as she describes their personal issues and how they come to cope with the time they must spend in the hospital. Through including personalized descriptions of supporting characters the reader generates an idea of how severe each of their circumstances are which in turn draws a dichotomy between Susanna and the other admittees. Susanna also introduces the reader to particular staff members, including Valerie, Dr. Wick and Mrs. McWilley. The staff members play a vital role in her awakening of whether or not the doctors have genuine intentions to successfully treat their patients due to the lack of health progression amongst her peers. Susanna and the other girls are eventually informed that the recently released Daisy died by suicide on her birthday. Daisy's death deeply saddens the girls and they hold a prolonged moment of silence in her memory.

Susanna reflects on the nature of her illness, including difficulty making sense of visual patterns, and suggests that sanity is a falsehood constructed to help the "healthy" feel "normal" in comparison. She also questions how doctors treat mental illness, and whether they are treating the brain or the mind. During her stay in the ward, Susanna also undergoes a period of depersonalization, where she bites open the flesh on her hand after she becomes terrified that she has "lost her bones". She develops a frantic obsession with the verification of this proposed reality and even insists on seeing an X-ray of herself to make sure. This hectic moment is described with shorter, choppy sentences that show Kaysen's state of mind and thought processes as she went through them. Also, during a trip to the dentist with Valerie, Susanna becomes frantic after she wakes from the general anesthesia, when no one will tell her how long she was unconscious, and she fears that she has lost time. Like the incident with her bones, Kaysen here also rapidly spirals into a panicky and obsessive state that is only ultimately calmed with medication.

After leaving McLean, Susanna mentions that she kept in touch with Georgina and eventually saw Lisa, now a single mother who was about to board the subway with her toddler son and seemed, although quirky, to be sane. Susanna's static mental health state and uncertainty about being "cured" when she is officially released from the institution sheds light on the subjectivity of mental illness. Individuals who exhibit emotions not commonly expressed are ostracized from society when in reality as humans we are all capable of experiencing mental health crises if strictly analyzed by a professional. Being "crazy" was her natural response to life's stressors at an especially vulnerable time dedicated to healing her inner child.

Structure
Girl, Interrupted does not follow a linear storyline, but instead the author provides personal stories through a series of short descriptions of events and personal reflections on why she was placed in the hospital. Kaysen works on encapsulating her experience by providing descriptive, concise illustrations of her time at the hospital as well as her own interpretation of the social classification of "insanity". She begins by talking about the concept of a parallel universe and how easy it is to slip into one, comparing insanity to an alternate world. Kaysen then details the doctor's visit before first going to the hospital and the taxi ride there at the beginning of the book before launching into the chronicles of her time at the hospital. She equates insanity in this instance with a mere alternate conception of reality; someone with mental illness possesses a different perception of the world as compared to an individual classified as neurotypical. She later discusses how some people fall into insanity gradually and others just snap. As discovered, her goal with the memoir is to overtly express how inculcated variations of mental illness are present in our daily lives and our social circles.

Characters
There are two main groups of characters, the patients and the staff. In addition to those there are her parents, her boyfriend and various other minor characters such as her former boss.

Patients

 * Susanna Kaysen
 * The autobiographical main character, Susanna Kaysen is admitted to a psychiatric ward to be treated for borderline personality disorder following a suicide attempt. She voluntarily admits herself after a short consultation with a psychiatrist who is also an acquaintance of the family. She is told that she will only be staying there for a few weeks, but it turns out to be one and a half years instead. Throughout the book, she frequently contrasts the time of the consultation, twenty minutes, to the time she ended up spending there.

 * Lisa Rowe
 * Lisa is diagnosed as a sociopath, but whether she actually is one is left open to interpretation. Lisa periodically escapes from the hospital, only to be found a day or two later and re-admitted. She is usually happy enough to be back though she does put up a fight when restrained. She is an ex-junkie who sleeps intermittently and barely eats, and enjoys making trouble for the staff. She apparently takes some pride in her diagnosis. Although she has a therapist assigned to her, she never actually sees him. Lisa is not in contact with her family except her brother, but the extent of their contact is not described. She also has a lawyer, though it appears he is mostly used to threaten the staff if she doesn't get what she wants. Her behavior is wildly unpredictable, and while she can be kind, she is also capable of cruelty towards the other patients. For example, Lisa has an ongoing rivalry with Lisa Cody that ends in Lisa Cody reverting to drugs.

 * Polly Clark
 * Polly is a disfigured patient who was hospitalized for schizophrenia and depression. Polly has severe scarring on her body, the result of setting herself on fire. According to Kaysen, because of the sheer guts it took to actually do it, Polly is highly respected for her courage, to the extent that none of the patients will ask why she did it. During her first year at the hospital, she appears calm and even cheerful: "Life was hellish, she knew that. But, her smile hinted, she'd burned all that out of her." But one day she suddenly breaks down and begins to scream inconsolably, as if realizing for the first time her appearance and the permanency of it. Kaysen then realizes that while the other patients might be released from the hospital, Polly is trapped forever in her scarred body.

 * Georgina Tuskin
 * Hospitalized for schizophrenia, Georgina is Susanna's roommate at the institution. The two of them are considered the healthiest patients on the ward and are good friends throughout the book. Georgina apparently experienced her first symptoms after an episode in a movie theater where she suddenly felt as if the darkness had surrounded her completely. It is not clear what the immediate reason for her diagnosis is. She also has a boyfriend in the hospital named Wade.

 * Lisa Cody
 * Lisa is admitted to the ward after Susanna, and from her first days there she looks up to Lisa Rowe. She, too, is diagnosed as a sociopath, though Rowe questions this and is clearly annoyed that she is no longer the only sociopath there. A former drug addict like Rowe, she tries hard to defend herself from Lisa Rowe's accusations that she isn't "real". She eventually escapes and is apparently found by Lisa Rowe during one of her escapes from the hospital. Lisa tells the other girls with pride that Lisa Cody has become a "real" drug addict. Her fate after her escape is not described any further.

 * Daisy Randone
 * Daisy is a thin girl who arrives before Thanksgiving each year, staying through Christmas. She has a single room, where she spends most of her time. The other girls think she is addicted to laxatives. She eats only chicken, and does so only in her room. However, after letting Lisa into her room, Lisa reports back to the rest of them that she only needs the laxatives because of all of the chicken. She peels off the meat and keeps the carcasses, saying that when she has 14 carcasses, it is time to leave the hospital, possibly due to obsessive–compulsive disorder. Daisy's father visits her quite often, and it is implied he has incestuous feelings for her. Daisy eventually commits suicide on her birthday. Susanna describes her as "sexy" and says Daisy had a spark that the rest of the girls lack. Daisy is reclusive and often refuses to be social. She hates it when anyone goes near her and is hostile when people approach her. However, she does allow Lisa to enter her room. Sometimes they even share cigarettes, indicating that Daisy does respect Lisa out of all the other patients on the ward.

 * Torrey
 * Torrey is a former drug addict. She was put into the ward after her parents discovered her promiscuity. She is the best friend of all the fellow patients. Her parents take her out against her will, and take her back to Mexico, where she believes she will become an amphetamine addict again. She describes Mexico, saying "being in Mexico means being dead and shooting speed to feel like you're not quite dead" (Kaysen, 97). The girls do try to help her with an escape plan and pool their money for her to help her, but eventually that plan is ruined, partly by Torrey herself, as she is too afraid to do it, and partly by Valerie after she gives Torrey a cup of thorazine just prior to her departure to calm her down. Though she only appears for a short time she is an important character. Kaysen distinguishes between those put there indefinitely by parents willing to pay without questioning the progress of their treatment and those whose parents are not willing to do so. Torrey is used as an example of the latter group.

 * Alice Calais
 * At first Alice seems quiet and, in Kaysen's words, "not too crazy"; but after about a month she breaks down and is taken to maximum security. When the girls go to visit her they find that she has painted herself and the walls in her seclusion room with her own feces. Most of the other patients believe she was "raised in a closet" because she is ignorant about the trivial things in life. For example, she has never tasted honey and doesn't know how it tastes. She is also completely unaware that her last name is a well-known location in France and is overwhelmed in awe when she hears of the Hundred Years' War. It is not explained what happens to her after the girls visit her.

 * Wade Barker
 * Wade, Georgina's boyfriend, is also a patient. Wade entertains the female patients with stories about his father, whom he claims to be a CIA agent with powerful friends involved in secret government conspiracies. The hospital regards Wade's beliefs as delusional. He is prone to violent outbursts, which eventually results in his being moved to the maximum-security ward. It is revealed that Wade's father's friends are G. Gordon Liddy and E. Howard Hunt, implying that Wade's father is Bernard Barker and that his delusions were based in fact.

 * Cynthia Crowley
 * A severely depressive patient who undergoes weekly electroconvulsive therapy. There are only a few references to her in the book and she isn't a major character in it.

Staff

 * Valerie
 * The head nurse on the ward. She works there during the day and though she can be strict she is generally liked by the patients and Kaysen in particular. She is described as down to earth and rarely uses the psychiatric terms used by the therapists, which is something that Susanna herself despises. Kaysen recalls her as honest and direct.

 * Mrs. McWilley
 * The evening nurse on the ward. Described as the exact opposite of Valerie and very much disliked by the patients. Kaysen recalls her as "clearly nuts". Valerie does not like her and tends to ignore her, although she does describe her as a professional when the patients complain to her.

 * Dr. Wick
 * The consultant psychiatrist. She is described as very old-fashioned and easy to embarrass. Susanna purposely tries to embarrass her, deliberately saying things that she knows Dr. Wick will react to, during their sessions together. She has previously worked in Africa and her direct contact with the patients is very limited, talking to them for only a matter of minutes in a session.

 * Melvin
 * Kaysen's late therapist and analyst. Susanna says that the two of them used to be good friends and that she once enjoyed sessions with him. According to her, he was old, balding, and slightly unattractive. Susanna would go into his office sometimes and just sit there in silence because there wasn't very much silence in the hospital and she needed a break. However, this relationship was short-lived; Melvin rolled into the hospital parking lot, and, when greeted enthusiastically by Susanna, refused to entertain her. Her opinion of him spiraled downward from that point.

title: Girl, Interrupted


text:
Talk:AMD64

FPU/MMX Registers
"Microsoft has chosen to not save the FPU/MMX registers across context switches in Windows XP 64-bit Edition for 64-bit programs "

Is this correct? I've seen quite a few MS blog entries supporting this claim but upon consulting the SDK from "Microsoft Platform SDK\Bin\win64\x86\AMD64\SWConventions.doc" Microsoft claims that MMX/Floating Point stack registers are preserved across context switches but MMX/FPU register use is stricly forbidden in kernel code.[section 2.3.7]

Perhaps this should read "...not save the FPU/MMX registers across 'all' context switches..." since I have no doubt it is (gladly) an attempt to obsolete FPU/MMX/3DNow instructions.

Bitbot 23:38, 16 October 2005 (UTC)

 * They're not saved across user/kernel transitions. They most definitely are saved across thread context swtiches. Fixed the article. Jeh 18:40, 5 December 2005 (UTC)

 * Ok, it seems someone else "corrected" things back. Fixed it again.  I did some more research on this... the FPU/MMX registers are not saved across u/k transistions, but this was the case under x86 too.  The real issue is that they are not saved when changing from, and are not restored when changing to, a thread that can only run in kernel mode.  For example, the threads in the so-called "system" process.  They most definitely ARE saved/restored when switching from/to all other threads, including threads running x64 code. I personally don't think all of these details belong in the article, as these are Windows internals details and the article is about AMD64, not Windows.... Jeh 04:55, 5 January 2006 (UTC)
 * Running x86/MMX/3DNow! instructions in 64-bit mode is not supported by AMD programming reference, the Windows SDK has no support for compiling both intrinsics and assembly code that uses these instructions on 64-bit plaform, so there's no need for Microsoft to support it. It's all outlined in Porting and Optimizing Applications on 64-bit Windows for AMD64 Architecture whitepaper right on the WHDC: 64-bit Platform site. And using math instructions in the kernel haven't been supported on ANY Windows platform, so there's no even need to notice.
 * But of course you're free to apply your "common sense" everywhere and remove any non-obvious content without even Googling the keywords first, all in all, it's a "free encyclopedia" you know (sarcasm). --DmitryKo 14:40, 9 January 2006 (UTC)
 * You have valid points and I focused too much on what the OS code is doing, and not on what developers should do. I've changed the Windows point accordingly, and just left out the whole issue of why... which is probably better for this page anyway.
 * Math instructions are perfectly usable in kernel mode in Windows in certain circumstances. That is what the DDIs KeSave/RestoreFloatingPointState are for (see DDK docs), or their Eng equivalents, the latter being available to graphics drivers (and very commonly used).
 * Finally, as for the CPU, the most recent version of the AMD programming docs ( from http://www.amd.com/us-en/Processors/TechnicalResources/0,,30_182_739_7044,00.html ) say "x87 floating-point instructions can be executed in any of the architecture’s operating modes" (volume 1, section 6.1.2) and "The x87 instructions can be used in legacy mode or long mode. Their use in long mode is available if the following CPUID function bit is set to 1:" (volume 5, section 2 intro -- and that bit IS set on my two Opterons and on my amd64). The same verbiage appears in the hardcopy versions I have, which are slightly older.  Do you have another reference that says otherwise? Jeh 01:06, 12 January 2006 (UTC)

And the issue continues...

Locke Cole added a comment to the article: " source for this ; I think early documentation indicated this was true, but in actual fact it's not? "

As DmitryKo pointed out above (and see the paper he linked at microsoft.com), it is not *supported* by Microsoft. None of the Microsoft compilers, etc., will generate x87 instructions, for example.

The early reports that were wrong were the claims that the OS would not save/restore x87 machine state in long mode. It does save and restore them, and furthermore x87 instructions will *work* in long mode. They'll even work in kernel mode in long mode, as long as you are careful to use the DDIs I mentioned. But MS doesn't support their use in long mode. Jeh 18:11, 15 January 2006 (UTC)

 * Thanks Jeh. The reason I mentioned it was that I'd read a blog entry on blogs.msdn.com (that I cannot find now) indicating that Microsoft had backpedaled on ditching FPU/MMX support. But obviously if I cannot find it, the article should stand as it is. =) —Locke Cole • t • c 18:29, 15 January 2006 (UTC)

And yet again...

In response to MirrorVax's deletion of the "they're not supported" statement I've added an amplified explanation. MirrorVax, if you have substantiation for the dispute, please post it here? Jeh 22:15, 16 January 2006 (UTC)

 * Well, you were the one doing the disputing. I'm agreeing with you. Mirror Vax 00:51, 17 January 2006 (UTC)

 * Oh, ah. I retracted that stance, at least as far as "what developers should do" is concerned. Probably I should have closed with that point instead of following it with "but, those opcodes WILL work!" Anyway I hope the main page is adequately clear now.

 * I'm still researching exactly why these instructions "aren't supported" -- but I have good reason to believe it has to do with stack usage and exception handling, as opposed to context switches. Jeh 01:19, 17 January 2006 (UTC)

Address Space Limits
About the claim :

"Due to the 64-bit architecture, the AMD64 architecture can address up to 256 tebibytes (also known as terabytes) of memory "

so 64 bits matches an 1.9... * 10^19, so about 19 Exa byte, so about 19'000'000 terabytes ! So could someone correct that claim or explain why the real addressing space is not as long as the theoretical addressing space ? If it's something like a practical adaptation to the largest size of memories in scope, it's a real shame, because I think we can't exclude Exabyte memories on a single computer, especialy because of the theoretical molecular limit of about 1.02 * 10^23 is still further away 5'000 greater which leaves 5'000 molecules for a mole of matter storing 19 Exa byte of memory, probably accessible with a volumetric memory based on nanotechnologies. Another reason would be the short life of a processor family making it unlikely to survive a 256'000 scale of memory evolution.

Best greetings LF

 * The AMD64 architecturally supports up to 252 bytes of physical memory and up to 264 bytes of virtual memory. Current implementation only supports 248 bytes of virtual memory and 252(AMD) or 240(Intel) bytes of physical memory. But the implementation limit could be lifted easily when necessary.Zuxy

Go read the Architecture manual, what you are saying is pure rubbish, the CPU supports a flat -non segmented virtual address space of 264 bits. Physically it handles 248 or 252 bits. Dont get the limits confused, what you are saying is highly erroneus. So in Virtual memory speak its 64-bits. —The preceding unsigned comment was added by Lordofacid (talk • contribs).

 * No, you are mistaken. Although virtual addresses are 64 bits wide, in current implementations (and for any chips known in the planning stages) you cannot populate that entire space. Valid ("canonical") virtual addresses run from 0 through 7FFF`FFFFFFFF, and from FFFF8000`00000000 through FFFFFFFF`FFFFFFFF. The high 16 bits of the address are ignored during address translation, except that they must be copies of bit 47 (in a manner akin to sign extension), or an exception will be raised.  So, although the addresses are indeed 64 bits wide, and all 64 bits must in fact be specified, only 48 of them are really usable.  This was done to cut down on the number of address translation steps, i.e. to reduce the cost of a TLB miss.  Hence 248, or 256 TiB usable virtual address space (of which 64-bit Windows is only populating a total of 16 TiB....) Jeh 19:06, 30 July 2006 (UTC)

 * ...updated the main page accordingly. I see a number of additional "implementation details" that could be added, such as page table entry format, a map showing the four-level (9 bits per level, plus 12 bits of byte offset in page = 48 bits total...) address translation scheme, details on how the REX prefix works, etc.  Then this new section would become a subsection under an "implementation details" section. Jeh 19:38, 30 July 2006 (UTC)

AFAIK 32 bit x86 CPUs support up to 32 + 16 - 2 (or maybe -3?) of Virtual memory space. 32 bit of offset, and (16 - 2) of segment (-2 because of the two priviledge level bits). True that this assumes flat memory (CS=DS=ES, etc.) is not used. Thus, 32 bit CPUs can access Virtual Memory space of 246, which can be accessed when running more than one process.

In practice, Windows 32bit, for example have the following [[limits]].
 * Wrong. At least in the 32-bit x86 architecture, the segmentation system doesn't allow access to more than 4 GiB (32 bits) of memory. This is because 1) the segmentation mechanism runs on top of the virtual address space, which is 32-bit, and 2) segments are not used like you assume: in real mode, "addresses" (offsets) can be 20 to 32 bits long (real/extended real mode), and the address is formed like this: segment*4 + offset. In protected mode, however, segments are defined by structures called segment descriptors stored in either the GDT or the LDT, and the address is formed like this: descriptor.base + offset. Those structures are 32-bit oriented, and thus won't allow addresses longer than 32 bits by themselves. The only way of having them is via the Physical Address Extension (PAE) mechanism, which allows the computer to have up to 36 bits of physicall addresses, mapped to the 32-bit virtual space using paging.

 * In the AMD64 architecture, however, and when in 64-bit long mode, addresses are always 64-bit, the segmentation mechanism is mainly deprecated (save GS and FS, of which only the base is used) and PAE paging is always enabled. The 256 TiB figure is because the AMD64 spec allows processors not to implement all the address bits: they can have as little as 48-bit of virtual addresses and 40 bits of underlying, paging-mapped physical addresses - current AMD64 processors are more or less like this. All addresses formed must be canonical as stated in the article, which, as the pictures explain, allow a neat positioning of both kernel and user code, not to talk of later extensibility. :Habbit 17:25, 19 September 2006 (UTC)

 * One could support 46-bit segmented addresses within a 32-bit linear address space; one cannot, however, have more than 232 bytes worth of the 246-byte segmented address space resident in the linear address space at any one time, so one would have to swap segments in and out of the linear address space in response to, for example, "segment not present" traps, and every reference to a swapped-out segment would involve a trap plus whatever operations are required to move other segments out of the address space to make room for the new segment to be moved in, as well as whatever operations are required to move the new segment in. That would be the case regardless of how much physical memory you have; all that additional physical memory would do for you would be to reduce the number of I/O operations to backing store required - it would not reduce the number of segment swap operations required.

 * So, in practice, while one could support a 246-byte address space, most, if not all, OSes don't bother. Guy Harris 06:17, 20 September 2006 (UTC)

 * Let's take a look at x86's way of translating a program-specified "memory address" into ones and zeros on the (max) 36-bit physical address bus, and how are some "usual" addresses specified and interpreted (you can check this in the Intel manual, order# 253668):

segmented address space (16b sel + 32b offset)   <--- any normal program address                    | segmentation                                                                                | linear address space (32-bit)                    <--- some special system addresses (i.e. GDT base) | paging and PAE                                                                                | physical address space (32 to 36-bit)            <--- CR3 base address                             \|/
 * Paging and PAE can be disabled, effectively skipping them (and limiting the physical space to 32 bits). So, in fact, you could design an operating system that allows each process to have some 16380 segments (i.e. using up all the descriptors in both the GDT and the LDT) of 4 GiB each, working with one at a time, and performing some gigantic page switches to allow accessing them all. That gives you an address space of nearly 32 + 14 = 46 bits, yep, but it's not worth the trouble of designing compilers with segmentation support, especially when you can have an AMD64 with a 48bit virtual address space (4 times the memory of your "46 bit" x86). Habbit 15:54, 20 September 2006 (UTC)

64-bit integer arithmetic
I think having native 64-bit integer arithmetic should also be mentioned in the "Some of the changes" list, because it's really one of the most fundamental changes (right?). intgr

 * You're right. Done. Jeh 18:40, 5 December 2005 (UTC)

Ancient History
Isn't the 8-bit processor 8085 and not 8088?

 * Well, the 8088 had an 8-bit data bus... --Brion 10:33 Jan 13, 2003 (UTC)

 * See, the page 8088 itself says 8088 was based on 8086, but this page seems to imply the opposite.

I hope the latest version clarifies the situation. 8080 -indirectly-> 8086, then 8086 --> 8088 --> 80x86 in general.

EM64T Not Identical?
Can someone substantiate the claim that EM64T is not entirely compatible with AMD64, and that it was based on an earlier revision of the AMD64 spec? If not, I think we ought to can it. --Doradus 15:33, 26 Aug 2004 (UTC)

 * Have a look at http://www.maximumpc.com/reprints/reprint_2004-04-07b.html Seems there are some subtle differences. Mhowkins 18:50, 26 Aug 2004 (UTC)

 * Thanks for the link. Unless I missed it, the article doesn't say what the differences are.  I know there are some system-level differences, but I'm not aware of any application-level differences. --Doradus 15:51, 28 Aug 2004 (UTC)

 * Ok, have a look at http://www.devx.com/amd/Article/20960, and http://www.infoworld.com/article/04/04/07/HNintelamdties_1.html

 * According to these articles, the Intel processors do not support the LAHF and SAHF instructions in 64-bit mode, because an early release of the AMD docs said the architecture would not. AMD later changed this statement, and support for these instructions was added to their processors. The other article implies that these instructions are used for context switching, so the difference is probably only relevant to O.S. kernel developers. Mhowkins 18:44, 28 Aug 2004 (UTC)

 * Interesting. My manuals at the office must be an older edition.  Looking at the specs freshly downloaded from AMD, they say nothing about LAHF being unsupported.  Thanks for the link.  --Doradus 02:09, 29 Aug 2004 (UTC)

The rewrite
(Doradus) Can anyone explain why the article was gutted and rewritten? I think the version before the rewrite was much better.

 * It seems like the user "Bad Byte" is the one who did this (and I later joined in, refining the separation of content). It was in an attempt to separate the earlier article into information about hardware implementing AMD64 and the AMD64 architecture itself. I think that the AMD64 article should be primarily about the AMD64 architecture, and articles like Athlon 64 and Opteron and Intel Xeon should be about the hardware implementing AMD64. However, as the hardware implementing AMD64 is relevant, I support the current list of products implementing AMD64, with links to the articles.

 * I think that the "supported operating systems" information from previous reincarnations of this article really needs to be brought back. That's important information this article shouldn't be without, and I think I'm going to get started writing this list.

 * Samrolken 17:23, 16 Oct 2004 (UTC)

(Doradus) Ok, sounds good to me. Carry on. :-)

Article title
AMD64 is centered around AMD. On the other hand, EM64T is centered around Intel. Why not just call it x64 and make AMD64 and EM64T redirects? - Sikon 15:24, 28 September 2005 (UTC)

 * As far as I know, "X64" is a Microsoft coinage. Some would say there are more than enough Microsoft-centric references in the article already. ;) Jeh 06:44, 6 December 2005 (UTC)

 * Why not call it x86-64, this way it doesn't show bias toward Microsoft, Intel or AMD. Coldpower27 23:47, 17 June 2006 (UTC)

 * The current organisation makes sense to me - AMD64 is the particular architecture designed and named as such by AMD, and thus this page is the primary source of information, while the EM64T article just talks about Intel's implementation of the architecture. -- intgr 01:44, 18 June 2006 (UTC)

Absolute garbage
What idiot mucked about with this page? This person clearly does not know one end of a PC from another. I can accept the world is full of ignorant and stupid people, but why oh why screw up a perfectly good page, and insert total nonsense? I've written tons of content for the PC section in the WIKI, AMD, NVIDI, ATI, so I'm not taking this lying down.

"...a straightforward extension of the x86 architecture to 64 bits"

Eh? So eliminating the FPU is just extending the x86 architecture? Er, no. Actually, its the biggest change to the x86 architecture since the i386 rolled out - and some would argue more significant. I'm going to put back a lot of the old content, my content, before the article got ruined and rendered technically inaccurate. I can't be bothered to find out who did this - whoever you are, read this, take note, put it down to experience, and take your ignorance elsewhere.

Right, done the deed. You know you have a crank, when stuff about AMD's advertising in the Netherlands, turns up in what should be a technical article. If we added a discussion of how AMD's CPUS are marketed in every country in the world, then where oh where would the madness end? Timharwoodx 20:38, 8 October 2005 (UTC)
 * Thanks for restoring the stuff with your 8 Oct edit. -R. S. Shaw 20:43, 10 October 2005 (UTC)

 * Sigh...I'm the one who attempted to clean up the article, only to have the nonsense and disorganization added back by Timharwoodx. That you write "tons of content" does not impress me. Your edits are, frankly, terrible. They are factually wrong, as well as wordy, opinionated, and disorganized.

 * Having made the damning charge above, I guess I have to give at least one example to illustrate the point. Consider: While it was considered at one point RISC chips would inevitably replace the outdated and quirky x86 architecture, in fact AMD64 effectively turns x86 into a modern RISC type programming environment. The genius of AMD64, is that it undertakes this major architecture upgrade, while retaining legacy compatibility. Total nonsense. To the extent it is something other than pure opinion/babble, it says that AMD64 includes a RISC-like instruction set. That is false, and it's a mistake that anyone with the slightest knowledge of the subject would not make.

 * Then we have the curious question above, "So eliminating the FPU is just extending the x86 architecture?" I can't make any sense of that. Again, total nonsense. Not even wrong. Mirror Vax 11:52, 27 November 2005 (UTC)

 * Having thought about it more, I conjecture that he is saying that AMD64 drops the x87/mmx instructions. That is false; they are included. Further, even if it were true, it would not be an earth-shattering development. SSE2 is not new with AMD64, remember. Mirror Vax 12:26, 27 November 2005 (UTC)

 * I agree with Mirror Vax (and I'm an old VAX hacker too!). More relevant: I actually work with AMD64 chips and systems at the OS kernel and device driver level. I've removed nearly all of the RISC references (there is utterly NOTHING RISC-like about AMD64!) and am gradually removing some of the rest of the apparent fanboism.  Jeh 18:45, 5 December 2005 (UTC)

Binary vs. Decimal prefixes
This article is confused on this point. For example, it says "256 terabytes", when the actual number is about 281 terabytes -- 256 tibibytes. In my edits this evening I tried to clarify things by adding the powers of two. Is that suitable? Jeh 17:02, 16 November 2005 (UTC)

What seems doubtfull to me
1) AMD64 (also x86-64 or x64) - x64 is Microsoft's term, not AMD's one. IMHO it would be consistent ether to remove non-AMD terms (AMD64 (former name: x86-64)) or include all the terms (AMD64 (also x86-64 or x64 or EM64T))

2) Marketing analizes section: AMD is told to never extend IA-32 instruction set. That is false! Remember 3DNow! and PowerNow! The real difference is that previously intel ignored AMD innovations and coupled them with it's own incompatible ones later (SSE instead of 3D Now! and SSE was told to be better technically, SpeedStep and later Enhanced SpeedStep instead of PowerNow! ST was worse, EST about the same), and for AMD64 intel did not developed it's own non-compatible 64-bit extensions. It is Intel's behavior that made difference, not AMD's one.

BTW, not the same is going about La Grande and VanderPool, but i would not say if it was AMD or Intel 1st in those extenseion and their analogues.

MS Biased article?
Does this article seem rather MS Biased? There are 12 references in this short article to "Windows", and 3 references to "Microsoft".

Compared to a single reference to the alternative operating systems that support the AMD64 instruction set. Seeing how MS was the last OS vendor to even support the architecture.....

 * This is a valid point.  I'm certainly not the person to do it; I'm a Windows kernel guy (and, in the past, a VMS kernel guy).  If someone wants to provide authoritative information on the details of how, for example, Linux, for example, uses AMD64's features, the "edit" button is up there for you to use. ;)

 * In that case I'd think the right thing would be to create a new section, "Operating system support", and gather all of the present refs to Windows support under there along with the new material. Hm.... Perhaps I'll do this anyway with the Windows material as it will clean up the existing text where it is now, and provide a good place for Linux (or other OS!) folks to add their stuff. Jeh 22:16, 5 December 2005 (UTC)

 * ... done, as far as Windows is concerned. Contributors other than me are needed to fill in the others.   Jeh 04:40, 13 December 2005 (UTC)

 * Heh... Considering the number of OSes out there, and the number of "OS vendors" in existence, I think it's more reasonable to say that Microsoft was one of the first to support x86-64. WinNT just came behind the major open-source *nixes, which is, I think, what you meant. -- uberpenguin 19:26, 13 December 2005 (UTC)

Removed features - V86 mode?
The "Removed features" paragraph says that Virtual-8086 mode was removed in 64 bit mode. Yet the chart right below it says that 16 bit applications are supported in the new 64 bit mode. What's the right answer? -- Myria 07:50, 23 December 2005 (UTC)

 * Note that Virtual-8086 mode and 16-bit code do not have to be the same.
 * V86 mode allows real mode apps (16-bit code) to run under protected mode, while protected mode can be 16-bit or 32-bit.
 * If in long mode it is able to run real mode code I don't know (Windows preferred to simply ignore it).
 * —Claunia 09:04, 23 December 2005 (UTC)
 * Did you confuse 32-bit processing with protected mode? 286 supported protected mode but was still 16-bit. Yuhong 06:45, 31 December 2005 (UTC)
 * See http://www.amd.com/us-en/assets/content_type/white_papers_and_tech_docs/24592.pdf, page 9

No-Execute bit
It should be noted that a similar feature has been available on 32-bit x86 processors since the 80286 as an attribute of segment descriptors.

The 80286 was 16-bit, not 32-bit. Do only 32-bit 80386 and up have segment descriptor attributes, or was it also in the 16-bit 80286?
 * MSTCrow 06:05, 25 December 2005 (UTC)

 * Ever since the 80286, x86 processors have always had two separate categories of segment registers - one for code and one for data. You can only ever execute from a "code" segment, meaning that "data" segments are never executable.  In fact, you cannot mark a "code" segment as writable, either.  In this way, Win16 is more protected against buffer overflows than Win32.  In Win32 and most other 32-bit operating systems, there is a separate code segment, but it maps to the same address as the data segment used in DS, ES, and SS, and segment registers aren't used for, well, segmenting memory anymore. -- Myria 23:54, 25 December 2005 (UTC)

Compare page
Can somebody do a compare page of AMD64 versus EM64T? I would really appreciate that, thanks! :)

 * See the EM64T page - in particular, see the Differences between AMD64 and EM64T section. Guy Harris 01:50, 4 February 2006 (UTC)

Links
I've added links to other wikipedia resources, please finish the work I started if i can't do it

(update) Opps, o forgot my sign

--Ciro07 11:42, 1 February 2006 (UTC)

 * You've added links to pages that already contain links in this article. There's really no need for such duplication - only the first occurrence of an article should be linked, and only if its relevant to the topic. I'm reverting all but one of these additions. Mind  matrix  16:41, 1 February 2006 (UTC)

AMD 64 problems in float computing
I have heard about the AMD 64 processers that they have problems in computing float numbers.If any one have any idea,I'll be be happy to know.Tanx.

Saham Hendinejad--Hendinejad 10:45, 23 April 2006 (UTC) [hendinejad@gmail.com]

 * What kind of problems, exactly? References? A quick google search turned up nothing relevant. If it's about errors, it's a problem with the specific CPU design and not the AMD64 architecture. Single- and double-precision floating point calculation of AMD64 and x86 is specified in the IEEE 754 standard. As for x86 full-precision (80-bit) FP arithmetic, the corner cases are pretty much unspecified and all programmers using these ought to be aware of potential issues. -- intgr 14:13, 23 April 2006 (UTC)
 * I think that is a reference to this news item, which affects certain "AMD Opteron 152, 154, 252, 254, 852 and 854 processors manufactured in late 2005 or early 2006", which are generally only used as server CPUs. -- Bovineone 22:40, 29 April 2006 (UTC)

Common Use vs. Stuff Nobody's Ever Heard Of
Honestly, now, who put Gibibyte in there? Is this a joke? —The preceding unsigned comment was added by 72.12.219.114 (talk • contribs).

 * I don't like it either. Your heading nailed it. The only reason I've not reverted it is because, sadly, consensus seems to be against us. jgp (T|C) 19:28, 28 June 2006 (UTC)
 * The wikipedia Manual Of Style says that the new prefixes are "recommended for use in all articles where binary capacities are used" -- Bovineone 04:54, 29 June 2006 (UTC)

 * Consensus against us?! If all wikipedia users were polled, I'd expect people to prefer what they see in a computer ad to what they see in the 37th page of an IEEE spec.  I guess it really comes down to accessibility vs. technical accuracy, and the intended audience.  How much jargon (gibibyte) should we let in, alienating the common man (gigabyte)? I hate the hard drive industry's power of ten lies as much as everybody else, but I really don't think this is how to fix it.  --Johnruble 18:45, 29 June 2006 (UTC)

 * Sorry but it is not the "hard drive industry's power of ten lies." "giga" means 1,000,000,000 and an 80 GB hard drive really does contain 80,000,000,000 end-user bytes -- usually a bit more.  And Windows will even show you that number, if you look in the disk properties.  Yes, in many Windows displays MS uses the "GB" prefix improperly, dividing  the drive capacity by 2^30 instead of by 10^9, showing the capacity as "73 GB"... nevertheless you can still store 80 billion of your bytes on the drive.  Tell me, would you still consider the HD makers liars if they put "80 billion bytes" on the box?  Er, wait, that's exactly what they're saying.  Jeh 23:12, 30 June 2006 (UTC)

 * Allow me to rephrase. Replace 'lies' with 'deception.'  The only place I've ever seen gigabyte used to portray one million bytes is on a hard drive box. --Johnruble 01:33, 2 July 2006 (UTC)

 * I'm sure you meant to type "to portray one billion bytes", but anyway... Turn it around: The only place that "giga" ever means 2^30 is when the prefix "giga" is followed by "byte."  What you're arguing is that it's perfectly fine for the same prefix to mean different things for different units of measurement:  One km should remain 1000 meters, a megawatt should be 1,000,000 watts, one GHz should still be 1,000,000,000 cycles per second... at least, I hope you would agree to those... but one GB should be 1,073,741,824 bytes.  That's frankly ridiculous, no matter how long the computer industry has promulgated it.  SI prefixes have been around just a *bit* longer, you know?

 * Furthermore there is no motivation to use binary prefixes with hard drives. There is absolutely nothing about a hard drive that requires or even encourages the capacity to come in powers of two (as there is with RAM), so why should a binary prefix be reasonable?

 * As for "deception," the only point of discrepancy is in the digits on the HD box vs. the digits displayed by Windows; after all, Windows WILL show you the capacity down to the byte, it does jibe with what's on the HD box, and it also jibes with the number of bytes Windows will let you store.

 * As for what people expect, ask a random sample of 100 PC users to write out the size of a "300 GB" hard drive without the "GB" and I'll bet 90% of them write "300,000,000,000 bytes." (If they are not sure how many zeroes the "G" prefix represents, ask them to try it with a "1.42 KB" file.)  Similarly, most people are not aware that a "256 MB" DIMM does not contain 256,000,000 bytes, but slightly more.

 * Personally I think it's the RAM makers -- and, of course, ALL displays in OSs -- that should change. Back when RAM was measured in KB the discrepancy was small, but at the GB level it's almost ten percent. And wouldn't the RAM makers love to change their labels to say, for example, "268 MB"?  Of course they would!  Everybody's reported installed RAM sizes would increase too.  It would be like a free upgrade!

 * You wrote "If all wikipedia users were polled, I'd expect people to prefer what they see in a computer ad to what they see in the 37th page of an IEEE spec." Don't you think Wikipedia should aim a bit higher than computer ads?

 * Seriously, the HD makers could address the issue very simply: in addition to saying "1 GB equals 1,000,000,000 bytes" on the box, they could also say (for a 300 GB drive) "this drive provides at least 300,000,000,000 bytes of usable storage (displayed by most operating systems as 279 GB)"  Jeh 03:02, 2 July 2006 (UTC)

 * The confusion between 1000 and 1024-base units has gone on long enough, and is becoming more and more important since the ratio between these units gets greater with larger prefixes. Introducing new units is the only real way to solve it, and I would expect most people to be intelligent enough to realize the relation between terms "megabyte" and "mebibyte" or much more so for MB vs MiB. These new units are also linked on most pages in case anyone is unsure. In my opinion, this is the way to go, and Wikipedia should be progressive in adopting new and positive initiatives. FYI, in addition to harddrive manufacturers, all networking hardware (eg, 100Mbit/s Ethernet meaning 100 000 000 bits) and internet connection speeds reported by most ISPs (not all, to add to the confusion) use 1000-base prefixes as well. -- intgr 11:07, 2 July 2006 (UTC)

 * re. comm speeds -- Exactly. Similarly, a "100GB native" LTO2 cartridge holds 100 x 10^9 bytes, not 100 x 2^30. So I was too broad above; "binary" prefixes are not even common with all uses with "bytes,"  it's really only "bytes of RAM" where they are used consistently.  There are just two possible solutions that make sense:  One, OSs should change to use binary prefixes in all displays where they are now using powers of 1024, and should display file and hard drive sizes with the correct decimal prefixes using powers-of-1000 divisors.  Or, two, OSs would change to use powers of 1000 in all cases, and RAM makers would relabel their products, so e.g. a "256 MB" DIMM becomes "268 MB." I actually like the latter solution better, as it maintains consistency. I think the RAM makers would like it too *grin*.  Jeh 13:06, 2 July 2006 (UTC)

You guys make good arguments. I suppose it's pretty ridiculous for me to wish to overload the definitions of metric prefixes when talking about bytes, though that's how I'd like it to be. Some day I'll have kids who have pebibyte ipods, and I'll be the old man, resisting change, refusing to start using the new prefixes. --Johnruble 19:08, 2 July 2006 (UTC)

Architectural features to tertiary headings?
I am looking at the "Architectural features" section and thinking that it would be much easier to edit if bolded items were subheadings. Would that upset anybody? It might (as in maybe, I don't really know) make merging easier. --Charles Gaudette 21:57, 3 September 2006 (UTC)

Shouldn't the date be mentioned
The article does not say when the 64-bit was introduced...

From my readings, it was first introduced as a concept in 2000, and produced in 2003 as Opteron and Athlon64

BUT, I'm not sure

Shabayek.com

title: Talk:AMD64


text:
Talk:Probability space

Simple events
Should we add into the article that simple events are independent? 134.71.66.237 (talk) 20:19, 24 September 2009 (UTC)

 * Intuitively, elementary events are independent, since the “nature” picks one and only one elementary event to become an outcome of the experiment. However from technical point of view we cannot say that {ω1} is independent from {ω2}, since these events are not necessarily in the σ-algebra of the probability space, and therefore they can be non-measurable.  …  st pasha  »  20:26, 24 September 2009 (UTC)

 * It is a common error, to confuse "independent' and "disjoint" ("mutually exclusive"). Elementary events are disjoint (well, provided that they are measurable...) and not at all independent. The probability of their intersection is equal to zero, not at all to the product of their probabilities. (Well, if one or both are of zero probability, then of course...) Boris Tsirelson (talk) 04:19, 25 September 2009 (UTC)

 * Ugh, shame on me :( such a noobish mistake. Of course they aren’t independent  …  st pasha  »  04:26, 25 September 2009 (UTC)

 * Why specify "elementary" event. Are there also non-elementary events? If so, how does an elementary event differ from a non-elementary event? Is "elementary event" a synonym for "outcome"? How does a simple event differ from an elementary event? —Preceding unsigned comment added by 80.133.111.96 (talk) 15:58, 9 March 2010 (UTC)

 * Maybe this terminology is somewhat archaic, but it exists outside Wikipedia, and we are not authorized to change it. The article contains a link to Elementary event; all your question are answered there. Boris Tsirelson (talk) 19:02, 9 March 2010 (UTC)

Relate
How does this relate to the concept of elementary event? - Patrick 10:20 Jan 13, 2003 (UTC)

Issues
A couple of issues: It would be nice if someone it it upon him- or herself to address these. Dbtfz 04:23, 19 January 2006 (UTC) Dbtfz 04:23, 19 January 2006 (UTC)
 * The article tries to explain the difference between Ω and S with some examples, but these do not really get to the heart of the matter. What is the difference, in general?  Is it that the elements of S must be (tuples of) measurable quantities?
 * The article notes that not all subsets of a probability space are events, but does not give an example or explain why this is so.
 * Example 2 is so verbose that its difficult to follow. I wonder if this could be replaced with easy to understand example. Example 1 is excellent but a bit trivial

Example 2 is quite easy to understand if you know all the terms (what a partition is, what a sigma-algebra is etc...). I do not think that it should be replaced by an easier example. Agreed - this example, though non-trivial, is excellent. The second part of example 2 is good, but it is not straight forward to see that the partitions are combined from the number of tails, which is the essence. The first part I cannot understand.

In fact, this is the problem that I have encountered in Wikipedia over and over again: make things easier so other people can understand. This can't happen because in that case you tend to make things less formal and mathematics should always be as formal as possible.

10:00, 25 August 2008 (UTC)

 * events typically are intervals like "between 60 and 65 meters" and unions of such intervals, but not "irrational numbers between 60 and 65 meters"

is WRONG, because by definition of a σ-algebra, if $$\mathcal{F}$$ contains, for example, all closed real intervals in $$[0,1]$$, then $$\mathcal{F}$$ also contains, for example, all irrational intervals in $$[0,1]$$. On a side-note, these irrational intervals are Lebesgue-measurable, so the above statement doesn't look good after the statement of
 * some of the subsets are simply not of interest, others cannot be “measured”

The (first noted) statement should be replaced with a correct reason for why $$\mathcal{F}$$ is not always chosen to be $$\mathcal{P}(S)$$.

-- anonymous12345678910111213141516 @ 2012-07-22 03:20:27 CEST — Preceding unsigned comment added by 78.92.204.127 (talk)

Symbol Pr
Speaking foundationally, the notation Pr is not more precise, as it obscures the fact that P is just a function like any other, and a situation using P for Probability and some other function is being inconsistent. Jfr26 11:18, 16 April 2006 (UTC)

 * P is here defined as a measure, with support on some appropriate sigma-algebra, while in my experience Pr(A) is literally shorthand for "the probability that A". Precise use of P—rather than Pr—is the goal, and speaking personally, I like Pr because it handily ties together a string of notational conventions, at the cost of one extra keystroke.  More to the point, it's commonly used for the above-described shorthand purpose by mathematicians and others and so deserves some additional explanation.   Ben Cairns 14:03, 27 April 2006 (UTC)

Merge
If someone can check that all of the relevant information has been moved to probability theory, we might be able to delete this page and replace it with a redirect? MisterSheik 17:12, 28 February 2007 (UTC)

 * Don't merge. There are too many articles which link specifically to Probability space for the specific material here, not for that material buried in a more general treatment.   Jheald 18:36, 3 March 2007 (UTC)

 * Is it a more general treatment though? Unless I'm missing something, the whole article on probability theory is just the definition of probability space.  The probability axioms are really part of the definition of probability space since they're restrictions on one of the components of a "probablity space".  What do you think?  MisterSheik 18:56, 3 March 2007 (UTC)

 * That may be part of the problem. Probability theory should be the top-level article for the whole of the mathematics associated with probability, as distinct from Probability broadly treating the question, "what is probability?".  Now the whole of the mathematics associated with probability theory is a much bigger subject than the definition of probability space, as any number of textbooks with the title "Theory of probability" indicate. Jheald 19:36, 3 March 2007 (UTC)

 * Regarding the probability axioms, I would treat them first, before introducing the full detail on probability spaces. The laws of probability apply perfectly well to probabilities of finite numbers of discrete events, and are most easily conveyed in that setting first, in terms of elementary events.  Only having treated the finite case first is it useful to generalise to the full works of measure theory and countably infinite sets - which may be beyond what some readers ever need to use. Jheald 22:23, 3 March 2007 (UTC)

Re-redirect probability measure ?
Suggest changing the redirect of probability measure to measure (mathematics), rather than here.

What do people think ? Jheald 21:29, 3 March 2007 (UTC)

 * For minor things like that, it is often better to just make the change and then discuss if someone cares enough to revert it (see WP:BRD). It saves a lot of discussion for things that are truly insignificant. CMummert · talk 00:58, 4 March 2007 (UTC)

I think that the redirect should be to here since a probability measure is defined on a probability space and not on an arbitrary measure space.

Topology Expert (talk) 10:02, 25 August 2008 (UTC)

Why start class?
Why is this article start class? It seems almost done. MisterSheik 23:58, 17 June 2007 (UTC)

 * The content is fine, but it could be more accessible. This does not mean it everything in the article should be understandable to everyman, but that each topic should be made as accessible as it can be. Geometry guy 00:08, 18 June 2007 (UTC)

 * I'm all for accessibility as long as it doesn't make things difficult for people that want to use the encyclopedia as a reference (as a opposed to a tutorial). That's why the examples are separated from the text.  I think maybe some better examples, and an extra paragraph to the lead would do it? MisterSheik 01:41, 18 June 2007 (UTC)

 * Sounds good. WP:LEAD (and more generally WP:MoS) contains lots of helpful advice (in case you haven't seen it). Geometry guy 11:11, 18 June 2007 (UTC)

First paragraph
Hi, I changed this: In probability theory, the definition of the probability space is the foundation of probability theory. to this: The definition of the probability space is the foundation of probability theory. which seems to make more sense.

It seems like there needs to be an informal (as accessible as possible and depending on as few specialized terms as necessary) definition of a Probability Space in that first paragraph though...

I don't know much about probability theory, and the fact that probability space is its foundation is an interesting fact, nevertheless it doesn't tell me what probability space is. —Preceding unsigned comment added by 157.193.108.159 (talk) 12:40, 26 October 2007 (UTC)

Usually?
It says "Usually, the events are the Lebesgue-measurable or Borel-measurable sets of real numbers." Shouldn't that be "If Omega is the set of real numbers (or R², R³ etc), then F is taken to be the Lebesgue-measurable or Borel-measurable sets". There are lots of applications of probability spaces which are based e.g. on a finite Omega.

Giese (talk) 09:45, 15 January 2008 (UTC)
 * Well, if the underlying space is finite, then every set is Borel, so it seems we're good either way. --Trovatore (talk) 22:25, 9 February 2009 (UTC)

Subset symbol
After the edit by 128.2.182.120, two notations are intermixed; see Subset. Compare $$ A \subseteq \Omega $$ and $$ \mathcal F \subset 2^\Omega $$; equality is permitted in both cases. Boris Tsirelson (talk) 21:08, 9 February 2009 (UTC)
 * Best would be to change all instances to $$\subseteq$$, unless (which I doubt, though I haven't checked) there is some place where it is necessary to specify that the inclusion is proper. In that unlikely case, it would be well to use $$\subsetneq$$; thus we avoid all ambiguity. --Trovatore (talk) 22:27, 9 February 2009 (UTC)
 * OK, I did so. Boris Tsirelson (talk) 07:14, 10 February 2009 (UTC)

What is wrong with the existing lead?
(An answer is expected first of all from User:Melcombe. Boris Tsirelson (talk) 20:23, 17 September 2009 (UTC))

 * So I made another lead, hopefully this time better than the previous one (or since according to somebody there was NO previous one, the new one must definitely be better than nothing :) ...  st pasha  » talk » 04:57, 18 September 2009 (UTC)

 * Now I see: it was an introduction rather than a lead. Boris Tsirelson (talk) 09:10, 18 September 2009 (UTC)

 * My interpretation of WP:LEAD, in this context, is that mathematics should be avoided where possible, and certainly that unexplained maths symbols should be avoided. I used the "missing" tag as what was there was clearly more appropriate, as it stood, to being an introduction section. What was there, and is now the "introduction", was far too heavily mathematical to be a lead. What is there now is much, much better, but some might still think is has too much maths. However, I suggest waiting to see if there are other complaints. My main concern now, in the lead and elsewhere, is the choice of font for "F" being used, at least I think it is meant to be an F. To me, there seems no reason to use particularly exotic fonts, especially where these turm out to be nearly illegible. Melcombe (talk) 09:14, 18 September 2009 (UTC)

 * However, use of just "F" (or rather F) here would contradict the tradition (in textbooks, monographs and papers). Boris Tsirelson (talk) 09:18, 18 September 2009 (UTC)
 * But can't we find an F more like the curly F I have seen and which I take as being the tradition. What I am presently seeing is a tiny set of black rectangles with a white line through them, which on a third or fourth attempt to work out what is one might just conclude is an F, in the absence of anything else it might be. Unfortunately my curent setup doesn't allow be to see what is available using the standard editting tools. Melcombe (talk) 09:29, 18 September 2009 (UTC)
 * Maybe, try "View->Zoom in" on your browser. Boris Tsirelson (talk) 09:33, 18 September 2009 (UTC)
 * I don't have that option, but when I change the font size to "larger" in IE7 I see that the symbol is an especially curly F. But for some reason "larger" is too large and I get little content on a screen, so I use "medium" which doesn't sound as if I am using an unusually small font. I did get the editing tools working again, but I don't see an acceptable F there, nor even any thing recognisable as the one presently being used. So how is it being added, and are there other choices for a replacement. I see that there some discussion of typography in Sigma-algebra. Melcombe (talk) 09:58, 18 September 2009 (UTC)

 * In order to change zoom in a browser you can try pressing Ctrl+ . As for the problem you describing, there seems to be a bug with Internet Explorer browser where it does not apply font smoothing correctly to certain Unicode characters. Another browser on the same system (that is, with the same (default) fonts installed) displays the curly “F” quite close to how TeX does it. See the screenshot (from Google Chrome browser):
 * Curly_F.gif
 * The symbol being used is a Unicode character SCRIPT CAPITAL F (U+2131), and it can be typed as &#x2131; (or simply copy-pasted) ...  st pasha  » talk » 16:37, 18 September 2009 (UTC)

(unindenting) Well yes, but MOS:MATH says "Although the symbols that correspond to named entities are very likely to be displayed correctly, a significant number of viewers will have problems seeing all the characters listed at Unicode Mathematical Operators. One way to guarantee that an uncommon symbol is rendered correctly for all readers is to force the symbol to display as an image, using the math environment." It is not just the F that I have trouble seeing, there also the R in R12 later on. It seems unwise/unhelpful to use characters not all can see. Melcombe (talk) 09:45, 21 September 2009 (UTC)

What is the problem with elementary sets?
In Example 4, elementary sets disappear; in Example 5 their occurrence is questioned by "clarification needed". Why? It is written in the "Non-atomic case" section: "Initially the probabilities are ascribed to some “elementary” sets (see the examples). Then a limiting procedure allows to ascribe probabilities to sets that are limits of sequences of elementary sets, or limits of limits, and so on. All these sets are the σ-algebra ℱ." Any problem here? In more technical words, elementary sets are a collection that generates the sigma-field, and are such that their probabilities are defined naturally. Boris Tsirelson (talk) 09:16, 18 September 2009 (UTC)

 * I never seen the term “elementary set” before, in our textbooks it was called “generator” set since it generates the σ-algebra. It appears to me that the use of word “elementary” here is to certain extent confusing: since we already defined elementary events as elements of Ω, and later on stated that the word “event” essentially means a subset of Ω. As such terms “elementary set” and “elementary event” appear to be synonyms, whereas in fact they aren’t. And this is the “problem with elementary sets” :) ...  st pasha  » talk » 17:09, 18 September 2009 (UTC)

 * You are right: it is my neologism, and poorly chosen. "Generator set"? Maybe. In which textbooks did you see it? Really, the whole collection of sets is generating; individual sets are not. But if it is already used in textbooks then it is the best choice. (Another option could be "simple sets".) Boris Tsirelson (talk) 16:06, 19 September 2009 (UTC)

 * In fact, "simple sets" is already in use, see Jordan measure. Boris Tsirelson (talk) 17:08, 17 November 2009 (UTC)

Comment on introduction
The new intro section starts "The probability space presents a model ...". My immediate thought was "the probability space for what?" ... what thing or what type of thing? Melcombe (talk) 09:20, 18 September 2009 (UTC)

 * Would you also ask "the linear space for what?", "the topological space for what?" etc.? It is not "space for something", it is a space serving as a model for something. (See also space (mathematics).) Boris Tsirelson (talk) 09:29, 18 September 2009 (UTC)

 * Yes I would. It should be either "the probaility space for a given scenario is ..." (i.e. "the" is specific (definite article), even if the topic is general) or "a probability space is ...." (i.e "a" is non-specific (indefinite article)). Recall that this is a general encyclopedia and should not descend into the misuse of grammar prevalent in much published literature. In addition the article has said anything useful about what a probability space is used for (a "general situation" is far too vague), so it really isn't just a case of switching "the" to "a". I suppose it might be "the probability space for a general situation is a only model ...  It would be better to have something first that says what aspects of "a general situation" are being modelled. Melcombe (talk) 09:12, 21 September 2009 (UTC)

Hello, I am an "idiot" who just edited the introduction without even looking at the discussion page. I was therefore unaware that the page was being edited very actively. Now I think I was a bit rude, like not seeing others in the room. Please do not be shy to edit what I wrote. Right now, I agree that the first words should be "A probability space is...". Cacadril (talk) 08:23, 27 September 2009 (UTC)

 * It’s ok, feel free to improve the article; we are currently distracted by “Normal distribution” anyways :)  …  st pasha  »  20:19, 27 September 2009 (UTC)

The lede
I am trying to figure out what exactly needs to be in the lede. What are the points to make, the ideas to conview, the misunderstandings to prevent? The issue of how exactly to word each point is secondary to this. The lede should be as concise as possible while still helping readers that do not know the particular perspective, or way of thinking, that is needed to make sense of the concepts. More detailed expositions belong in the sections below the lede. Still some details may be a good idea to include in the lede becase they help the unprepared reader to make sense of it. As the lede stands now, I feel it may be a bit too wordy, and some of it could be moved to the introduction. As suggested by another contributor above, the lede should state what the subject is (a combination of three things), not just what it does (models situations) or what it is useful for. Still some such information is helpful for the unprepared reader because it defines the perspective. I am considering: In probability theory, a probability space or a probability triple is a mathematical construct that models how the laws of probability apply in situations where there are multiple things that can happen next. A probability space is constructed with a specific kind of situation or experiment in mind. One imagines that each time a situation of that kind arises, the set of possible outcomes is the same and the probability levels are also the same. A probability space consists of three parts: A set of distinct possible outcomes; a set of groups of outcomes, called "events" to which specific probability levels are assigned; and the assignment of probabilities to these groups, i.e. a function from events to probability levels. Cacadril (talk) 10:39, 27 September 2009 (UTC)

nature makes its move

 * Once the probability space is established, it is assumed that “nature” makes its move and selects a single outcome, ω, from the sample space Ω. Then we say that all events from $$\scriptstyle \mathcal{F}$$ containing the selected outcome ω (recall that each event is a subset of Ω) “have occurred”. The selection performed by nature is done in such a way that if we were to repeat the experiment an infinite number of times, the relative frequencies of occurrence of each of the events would have coincided with the probabilities prescribed by the function P.

This seems very muddled--is there a more formal description of what happens here? For example, if I repeatedly flip an unbiased coin (infinite Bernoulli process) and "nature" selects the sequence H,T,H,T,H,T... then the frequencies of occurrence coincide with the expected 50% heads, but I wouldn't call it random. Thanks. 66.127.52.47 (talk) 01:29, 14 April 2010 (UTC)

Standard probability space
It would be good to have a few sentences to link to Standard probability space, rather than just having this under "see also". It seems a good thing to give a mention to in this article, given the overlap of names. Melcombe (talk) 11:56, 9 September 2010 (UTC)

 * I did; please look now. Boris Tsirelson (talk) 13:40, 9 September 2010 (UTC)

 * Is that all that can reasonably be said? I guess the name suggests that the idea is more important than you have made it sound. Melcombe (talk) 15:15, 9 September 2010 (UTC)

 * I like that notion, but I do not want to exaggerate. When we only consider random variables, their distributions, operations (sum etc), all probability spaces are equally good. This is why elementary textbooks never mention standard prob. spaces. Their advantage appears only when we start dealing with regular conditional probabilities, and/or measure preserving transformations. However, these topics are more advanced than the "prob. space" article, devoted mostly to the discrete case. The name suggests? I did not choose the name "standard"; it is chosen by others, outside Wikipedia. It means only what it means. Boris Tsirelson (talk) 15:42, 9 September 2010 (UTC)

 * That's why I leave it to those who have a proper understanding to decide these things. The immediate question was just, in the spirit of being helpful to readers, what pointers to other articles should this one contain. After all, part of the point of wikipedia is the interlinking between articles: "if you're interested in this, then you might be interested in that". Melcombe (talk) 09:03, 10 September 2010 (UTC)

Weird sentence in introduction
Can this sentence be rewritten? "If the outcome is the element of the elementary event of two pips on the first die and five on the second, then both of the events of "7 pips" and "odd number of pips" have also happened."

The concepts "element" and "elementary event" weren't introduced before in the text. Wisapi (talk) 00:29, 13 September 2010 (UTC)

Zero/One probability
"A probability is a real number between zero (the event cannot happen in any trial) and one (the event must happen in every trial)." Is it true that if the probability is zero (one) the event can never (must always) happen? If X is drawn from a uniform distribution in [0,1], then P(X = 1/2) = 0 and P(X != 1/2) = 1, but X can be 1/2. Am I wrong? If I am, I think I might not be the only one. Could we explain it a bit. 71.232.61.24 (talk) 02:03, 6 May 2011 (UTC)
 * Good catch. The text as written is simply wrong.  If no one else gets there first I'll fix it (the right fix might need some thought). --Trovatore (talk) 02:06, 6 May 2011 (UTC)

Conditional Probability Given The Empty Set
The article states that conditional probabilities can only be defined using conditions that have non-zero probabilities. If A,B,C are sets in a probability space and B and C are disjoint, the value of P(A| B intersection C) is thus undefined. I think there are many practical situations where P(A| empty set) could be defined to be zero, as long as we are dealing with the equation P(A | W) P(W) = P(A intersection W) and not an equation involving division by W. If the set W is defined by scalar variables, I suppose this would be a case of filling-in the discontinuity of a function rather than extending the theory of probability spaces. However, this topic deserves attention in some article on probability theory and this articles seems as good a place as any.

Tashiro (talk) 16:25, 10 June 2011 (UTC)

A related issue: after choosing out a set A and defining conditional probability, the article points out that this too is a measure. But it does not say on what space it is a measure. Surely not on the original sample space, since the measure is defined only for supersets of A. Shouldn't the article state how to construct the entire triplet (sample space, sigma-algebra, measure) for this new measure? 66.167.204.18 (talk) 07:43, 14 June 2014 (UTC)

 * "Surely not on the original sample space, since the measure is defined only for supersets of A." — First, you probably mean "for subsets of A". Second, do not be sure! It is defined on the original sample space! (Otherwise, if B is assumed to be a subset of A, why the intersection in the numerator?) Yes, it is possible to construct the entire triplet for this new measure. However, the complement of A is of conditional probability zero, thus, it is harmless. Moreover, it is convenient that we may say "the conditional probability of the second 'head' given the first 'head' is 1/2"; here, B is neither a superset nor a subset of A. Boris Tsirelson (talk) 08:03, 14 June 2014 (UTC)

Definition of the σ-algebra
I don't think that the property "F contains the empty set: ∅∈F" is necessary for defining F, because: The fact that both ∅ and Ω belong to F could be additional corollaries of the two other properties. — Preceding unsigned comment added by 137.132.250.14 (talk) 03:56, 16 January 2012 (UTC)
 * From the complement rule: for any A∈F, we also have (Ω∖A)∈F
 * From the union rule: (A∪(Ω∖A))∈F so Ω∈F
 * From the complement rule again: Ω∈F so ((Ω∖Ω)=∅)∈F

 * Yes, but then you need F to be not empty. Is it better? Boris Tsirelson (talk) 06:28, 16 January 2012 (UTC)

Congratulations
Oh..my..God; a statistics article on wikipedia which is understandable. This Friday is getting better and better. I'm going to indulge myself now, if you don't mind. — Preceding unsigned comment added by 145.18.213.196 (talk) 09:37, 1 March 2013 (UTC)

A big thank you..
Thank you for contributing to my ability to understand by providing such clear definitions of concepts that within research papers simply get assumed as known. Not sure how I could hope to survive as an academic without Wikipedia.

Ijdavis (talk) 04:10, 6 April 2014 (UTC)

Oops!
The die pictured is incorrect; opposite faces always add to six. — Preceding unsigned comment added by 2601:0:e00:f8ab:7cc0:ec3d:e020:f354 (talk • contribs) 22:34, 8 July 2015
 * No, opposite faces add to seven. If they added to six, then you'd have three pairs of faces adding to six, which means the total number of pips on a die would be 18.  But 1+2+3+4+5+6 is 21, not 18. --Trovatore (talk) 22:38, 8 July 2015 (UTC)

Use math tag for typesetting mathematics
Instead of trying to use Unicode characters, which often ends up looking really "funky", I suggest using the math tag and appropriate LaTeX commands. I have done this in the introduction, which looks a whole lot better. Do you not agree?Kdmckale (talk) 00:13, 29 September 2015 (UTC)
 * Hmm — your version actually does look pretty good on my screen. (But I may be using some experimental preferences; I'd have to check.)
 * In general we discourage inline LaTeX because it creates PNG images that don't resize well and throw off the linespacing. I suspect that the only reason that isn't happening for your case is that you're only using single characters rather than more complex typesetting.  --Trovatore (talk) 00:40, 29 September 2015 (UTC)

Random Experiment Establishes Sample Space
Its much more intuitive to say the random experiment determines the outcome space than to say there is an outcome space associated with a random experiment. Its difficult to grasp why we should discuss outcome spaces but its not difficult to grasp once we assume a random experiment is performed. For instance, if the experiment is rolling a six-sided die, then the experiment determines a sample space with 6 outcomes. Mrdthree (talk) 23:56, 2 May 2016 (UTC)

The chicken or the egg?
The selection ($$\omega \in \Omega)$$ performed by nature is done in such a way that if the experiment were to be repeated an infinite number of times, the relative frequencies of occurrence of each of the events would coincide with the probabilities prescribed by the function $$P$$.

The choice ($P$) made by mankind is such that if the experiment were to be repeated an infinite number of times, the relative frequencies of occurrence of each of the events would coincide with the probabilities prescribed by the function $P$. (Probably... )

I don't think nature is concerned with our experiments in its selection process. YohanN7 (talk) 09:25, 23 May 2016 (UTC)

 * (But why not sign?..)
 * Yes, philosophically, we could try to imagine "the" universal probability space established by nature itself, once and for all (of which all our "small" probability spaces are quotient spaces). But I am afraid that this "grand design" is neither free of conceptual problems, nor useful in practice, nor helpful pedagogically. Boris Tsirelson (talk) 09:10, 23 May 2016 (UTC)

Example 2
I found this formulation confusing:

 * Alice knows the outcome of the second toss only.

How about
 * Alice is concerned with the outcome of the second toss only. The events interesting her are described by the partition Ω = A1 ⊔ A2 = {HHH, HHT, THH, THT} ⊔ {HTH, HTT, TTH, TTT}, ... Likewise for bob who would then be concerned with the number of tails, not knowing it. YohanN7 (talk) 10:06, 24 May 2016 (UTC)

 * (But why no signature, still?..)
 * I see your point... But it is usual to describe partial knowledge by σ-algebras. For Alice (that knows the outcome of the second toss only) the expected value of a random variable is its conditional expectation on her σ-algebra (and the variance is the conditional one). In game (or economic) theory, your expectation of the exchange rate (dollar/euro, say) of tomorrow is its conditional expectation on your σ-algebra of today. "Concerned" looks for me a more exotic situation. How to explain it to the reader? Boris Tsirelson (talk) 20:22, 23 May 2016 (UTC)
 * Obviously we interpret the word "knows" differently. If she really knows the outcome of the second toss, say "tails", there is either nothing left for her to say being unaware that there had been other tosses or, if she is aware that other tosses were made, only the set A2 = {HTH, HTT, TTH, TTT} would interest her. Might it be said that she is unaware about everything else than toss #2 rather than knowing the outcome of "2? YohanN7 (talk) 10:06, 24 May 2016 (UTC)
 * ... or that she can measure #2 only? YohanN7 (talk) 10:11, 24 May 2016 (UTC)
 * Ah, yes, when I say "Alice knows the outcome of the second toss", I really mean "and only this"; and in every case I mean that all nonrandom things are common knowledge anyway (that is: what will be tossed, how many times, etc). Maybe all that should be stated explicitly. Boris Tsirelson (talk) 11:53, 24 May 2016 (UTC)

 * And by the way, the formula P({ω ∈ Ω: X(ω) ∈ A ⊂ S}) looks for me somewhat strange, like P({ω ∈ Ω: X(ω) = 0 < 1}). Again, I see your point, but... Boris Tsirelson (talk) 20:26, 23 May 2016 (UTC)

 * Okay, if $A ⊄ S$, then it is false. But i really though that that was the case, or do you mean I state the obvious? Also, we cannot really have both $X ∈ A$ and $A ⊄ S$ because $X ∈ S^{Ω}$. Either which way, there is some notational abuse involved that needs to be explained unambiguoulsy. YohanN7 (talk) 10:06, 24 May 2016 (UTC)
 * Now better. I meant that in a formula of the form {ω ∈ Ω: P(ω)} I expect a predicate P of ω (only); any condition on something else (say, A) is better placed outside the braces. Boris Tsirelson (talk) 11:53, 24 May 2016 (UTC)

Alternative approaches
The introductory part ends as "In modern probability theory there are a number of alternative approaches for axiomatization — for example, algebra of random variables." This seems to be a strong overstatement. For example, AFAIK the “random variables” cannot cover the more delicate (but rather important) questions like dependence on filtrations in random processes, predictablity etc.

I think this should be clarifying by adding something like “axiomatization of the simplest aspects of this approach”. --Ilya-zz (talk) 06:37, 16 March 2021 (UTC)

title: Talk:Probability space