Talk:Standard probability space

message: * The first two "pro & con" sections should either disappear or be moved under the section called "Using the standardness".  This is not an article about legalizing abortion or drugs; it's just a mathematical concept.
* The attempt to define "pathologic" might go a lot easier if a standard probability space were defined first and then a probability space were said to be "pathological" if it is not standard.  A section giving some motivation for a formal definition of standard probability space would be appropriate in its place, but it is futile to attempt to exhaustively cover every case that might be considered pathological or "non-standard" in some vague undefined sense.
* The formal definition(s) of a standard probability space should be given more prominence in the article, and perhaps elaborated upon some more.  This is, or should be, after all, the main point of the article. 
* History should go after the definition.  I want to know what it is before I care to read about its history.
* The general tone/style of writing may be a little too informal in a few places. (A very minor issue here.)
* Contributors should try to avoid citing their own works (unless, of course, they are published in a peer-reviewed journal.)
Deepmath (talk) 02:05, 26 August 2008 (UTC)
replies: text: Thank you for the criticism; I'll think on it. Boris Tsirelson (talk) 07:02, 26 August 2008 (UTC)

text: I did, according to the opinion of Deepmath, in spite of my suspicion that some wikipedians think differently. Well, they may participate, too. Boris Tsirelson (talk) 12:32, 26 August 2008 (UTC)

text: Now I have nothing to voice. My doubts (reservations, objections) are already voiced by you! Your new suggestions do not raise new doubts. I try to implement them. Boris Tsirelson (talk) 17:30, 27 August 2008 (UTC)

text: The next iteration is made; please look. I know that something remains to do (especially, some more equivalent definitions). At this point, however, let me remind to you and all, that I am just the initiator, not the owner of the article. Start making your improvements yourself! Boris Tsirelson (talk) 19:40, 27 August 2008 (UTC)
replies: text:  I'm going to take a break for a while, but I should be back next week.  I'm still trying to get a better handle on completeness vs. regularity for probability measures, which seem to be mutually exclusive on a separable space, unless I'm not understanding something quite correctly.  I'll have to do some more research so I actually know what I'm talking about before I can actually contribute much to this article.  For example, I'm suspecting that if a measurable space admits a complete measure, it might in fact have "too many" measurable sets in its σ-algebra to have the regular conditional probability property.  But there might be some sort of correspondence I'm overlooking here, and there almost certainly is, if you insist that a standard probability measure be the completion of a Borel measure.  I did change the remark you made to that effect in that article, but I think (I know) it's still not right, so feel free to fix it.   Deepmath (talk) 00:35, 28 August 2008 (UTC)
replies: text:  Yes, I fixed it. You should not just say that a measurable space is Radon, for a trivial reason: A measurable space itself is not a topological space, while to be Radon or not is defined for topological spaces only. Boris Tsirelson (talk) 08:01, 28 August 2008 (UTC)
thread_title:  Article needs major rewrite 

message: "...seem to be mutually exclusive on a separable space..." --- Why? If regularity holds before completion, then it still holds after completion. Indeed, you add/subtract a null set; and the null set is included into an open set of arbitrarily small measure... Boris Tsirelson (talk) 08:14, 28 August 2008 (UTC)
thread_title:  Completeness vs. regularity for probability measures 

message: I know that in general I should not change the style of references chosen by other editors. But hopefully I may change the style of references chosen by myself! Boris Tsirelson (talk) 16:06, 27 April 2009 (UTC)
thread_title:  References style 

message: "He constructed the Wiener process (also called Brownian motion) in the form of a measurable map from the unit interval to the space of continuous functions."
This sentence is in the introduction, but there is no indication how it relates to a standard probability space. Presumably Brownian motion is defined on such a space? 192.41.132.250 (talk) 14:32, 16 May 2023 (UTC)
thread_title:  This sentence is unexplained 

message: The example in the section "A naive white noise" -- why is this an example of a non-standard probability space? It looks pathological or useless, but how does it concretely violate the requirement? 
Also, why isn't the set 
: \displaystyle S(f) = \{ x : |f(x)| > 0 \}
countable with probability 1? So f would be measurable with integral zero 
with probability 1.
2A02:1210:2642:4A00:25F2:D4AE:35CC:D1E5 (talk) 18:57, 16 May 2023 (UTC)
thread_title:  This section fails to connect