Talk:Convergence of measures

message: From the point of view of a general encyclopedia reader, this page is complete gibberish. If you have to be a statistician to understand an encyclopedia entry on a statistical item of interest, what's the point?
Why not a simple explanation using two six-sided dice - showing how while the result on each die is random, the sum of the dice converges on a mean of 7?  —Preceding unsigned comment added by Tom Adams (talk • contribs) 23:14, 30 April 2009 (UTC)
replies: text: This page is about the measure-theoretic concept. If you want a more lay-person explanation, see the “Convergence of random variables” article.  … stpasha »  06:29, 21 November 2009 (UTC)

text: Although that page is also pretty lousy, from a lay-person perspective.--128.59.110.50 (talk) 00:29, 17 February 2010 (UTC)

text: Agreed. Even as a physicist I don't understand the contents of this entry. As a scientist, I found this explanation utterly useless as an every-day "pedestrian" type definition, and it doesn't belong in this form in an encyclopedia (Wikipedia is not an encyclopedia written by mathematicians to themselves ...). You should at least add an intuitive explanation of the concept. (BTW, so far I have not found any good mathematician who would be short of giving an intuitive explanation for a definition - even mathematicians need those at times!)
--134.76.219.87 (talk) 16:10, 15 June 2010 (UTC)
thread_title:  Boo 

message: In the list of equivalences, does E denote expectation with respect to P?  This should be specified, I think.98.99.129.198 (talk) 00:30, 15 February 2012 (UTC)
replies: text:  Yes, fixed now (I am not sure how to find a reference for it though: this is basically the so called Portmanteau lemma (sometimes called theorem) which would be presented using different notation in different books.  Piyush (talk) 06:41, 23 July 2012 (UTC)
replies: text: After many many years on WP, I have realized that one of the greatest things we can do here is to provide a 'rosetta stone' translating across different notations.  I've had this problem, where theorems I might recognize, when written from a measure-theoretic point of view, become utterly foreign and strange looking, when written with using random variables. It gets even worse if there is some overlap to quantum stuff, or with projective varieties or whatever.  So repeating a claim, in alternative notations, is a good thing. linas (talk) 18:35, 24 July 2012 (UTC)
thread_title:  Undefined symbol 

message: Anyone care to start an article on the d-bar distance or d-bar metric?  I'm reading about this now; its used in the theory of dynamical systems, and it seems to be maybe related to the Wasserstein metric, if not maybe identical to it in some or another case.  I'll see if I can figure this all out in the next few...days? months? Its needed to define a finitely-determined process.  linas (talk) 04:19, 29 July 2012 (UTC)
thread_title:  dbar distance

message: More clarification is needed. The article currently states that 
:lim P_n(A) = P(A) for all continuity sets A of measure P.
is a variant definition of weak convergence.  But if I remove the word 'continuity' in the above, then I get the definition of strong convergence. I'm trying to think of a good example where the two are inequivalent, and where its obvious that the continuity sets were the cause of the inequivalence... having this example in the text would be nice. linas (talk) 16:25, 29 July 2012 (UTC)
thread_title:  Portmanteau thm 

message: I rewrote this section a bit to, hopefully, make it more clear, as well as moved it further down because it uses vague convergence. AnnZMath (talk) 14:21, 8 October 2023 (UTC)
thread_title:  Section Weak convergence of measures as an example of weak-* convergence 

message: As of Bourbaki the vague convergence is a convergence resp. of space C_c, and not C_0. Bourbaki, Integration, Ch. III.  — Preceding unsigned comment added by 141.43.110.155 (talk) 20:12, 25 April 2024 (UTC)
replies: text: I'm not very familiar with this, because I mostly work with probability measures (and in that case taking C_c or C_0 makes no difference). But the definition using C_c does indeed seem to be the most common one so I am going to fix the article. Malparti (talk) 16:39, 29 April 2024 (UTC)
thread_title:  Section Comparison of convergence