This page is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
Edit history was combined with that of Mathematical measure on 2003 Mar 11; the move that broke the history was made on 2002 Oct 26.
This article appears to switch notation about half-way through, from X to S; please see discussion at Talk:Sigma-algebra#Notation. linas 14:11, 25 August 2005 (UTC)
The discussion pages on measure theory -- site to site -- has formed a loop with no information!
Hey, everyone, let's post an example of a non-measurabe set! (unless I missed where it was discussed on Wikipedia...)
Sorry, forgot to sign in -- MathStatWoman anonymous post on 22 dec 2005
I think the non-measureable set term in the section of counterexamples should be emphasize to Lebesgue non-measurable sets ... e.g. Vitali set is not Lebesgue measurable because two properties of translational invariance and countably additivity are inconsistency. The Vitali set may be measurable for other measures that does not requite both two properties .... Jung dalglish 19:12, 3 February 2006 (UTC)
The section Formal definitions currently starts with the following sentence:
The section then continues to define countably additive measures. Do mathematicians always mean countably additive measures when they refer to measures without further qualifications? If yes, this should be stated early on. As the article stands now, the unqualified notion of a measure is never formally defined. (At my first reading of the section I was always expecting a sentence starting with "A measure is then constructed from a countably additive measure by..." or similar.) — Tobias Bergemann 16:11, 16 January 2006 (UTC)
Right now, the material at σ-finite measure seems to be a verbatim copy of the material in the corresponding section of this article. I think splitting off sections is a good idea only when an article gets too long. Thus when some analyst comes here and writes us a book on σ-finiteness, we should split it off, but until that day, we should keep all our articles intact. Therefore I propose changing it to a redirect. I request your comments. - lethe talk + 21:09, 11 March 2006 (UTC)
It is rough for math neophytes to look at formulas first thing off, could it be possible to give more information on these formula... if possible. For the rest, it seems good. Lincher 15:20, 2 June 2006 (UTC)
Should a measure be defined on a semi-ring, then using Carathéodory's extension theorem show that the measure can be extended? — Preceding unsigned comment added by Mikemtha ( talk • contribs) 23:01, 24 October 2006 (UTC)
I changed the section heading for Counterexamples to Non-Measurable Sets and added a 'main article' link to that article (Which, by the way, I'm not a fan of but...) Zero sharp 21:46, 3 November 2006 (UTC)
The Opening says:
In mathematics, a measure is a function that assigns a number, e.g., a "size", "volume", or "probability", to subsets of a given set. The concept has developed in connection with a desire to carry out integration over arbitrary sets rather than on an interval as traditionally done, and is important in mathematical analysis and probability theory.
The introduction is meant to be informal, and I think it does the job well. It gives the idea that each set is mapped to a number. Further details and a more formal definition is supplied below in the text. Oleg Alexandrov ( talk) 02:43, 3 August 2007 (UTC)
I believe the recent changes to the intro made it too complicated and confusing. The first several sentences of an article are very important, and it is important that they are clear and to the point, rather than comprehensive. There is too much repetition now, see sentences 1 and 3. Comments? Oleg Alexandrov ( talk) 02:56, 6 August 2007 (UTC)
Can someone please add a section on the practical applications of measure theory? My interviews with a broad range of scientists suggests that measure theory has a zero measure of contribution to any sort of applied science. —Preceding unsigned comment added by 24.226.30.183 ( talk) 05:16, 18 January 2008 (UTC)
This article is pretty much nonsense at the moment. Being a measure theorist, I am surprised how this article got to GA in the first place (but now it is demoted). The point is that many of the important topics in measure theory are non included not to mention that the lede is not up to par (politely speaking). I will start a rewrite now. PST
Why μ(Ø) = 0 appears as part of the definition?! It follows from additivity, doesn't it? Maybe it should be moved down as note? Vasili Galka ( talk) 17:32, 24 June 2009 (UTC)
Actually it's not necessarily redundant. It depends on the meaning of 'countable collection'. Some use 'countable' to mean 'infinitely countable', and σ-additivity usually does refer to the infinite case. In such case, the above proof of the second axiom from the third doesn't pass, and in fact one has to rely on the second to deduce finite additivity from σ-additivity. bungalo ( talk) 21:09, 27 June 2012 (UTC)
User:Finell on 21 July 2009 required inline citations. However, "Editors making a challenge should have reason to believe the material is contentious, false, or otherwise inappropriate", according to Wikipedia:When to cite#Challenging another user's edits. Is it the case here? Could Finell be more specific, pointing to a problem? Boris Tsirelson ( talk) 19:08, 18 August 2009 (UTC)
The definition claims that Σ is a σ-algebra, that μ is a function on Σ, and that but if you click on the link to σ-algebra you'll find the first point in the definition of a σ-algebra that it must be non-empty. So shouldn't be in the domain of , making the second point in the definition apparent nonsense. Would knowledgeable someone please clear this up. Pulu ( talk) 23:23, 8 October 2010 (UTC)
I just read through the lead on this article and I think it stands as a model of how to make a comprehensible lead for a potentially very technical subject. Good work! Benwing ( talk) 05:09, 21 October 2010 (UTC)
1. There is not a single citation.
2. In particular, re: "a mysterious function called the "mean width", a misnomer." Provide citations for who used the term and who stated it is a misnomer. Also, is this good mathematical writing? Michael P. Barnett ( talk) 21:14, 3 May 2011 (UTC)
The pair is called a measurable space -- is undefined. — Preceding unsigned comment added by 193.219.42.53 ( talk) 10:59, 19 November 2012 (UTC)
Contrary to what is stated in the article, "measurable function" is defined to be a function that has f^{-1}(G) measurable for every open (or closed) set G. This meaning of the notion is the usual one from pure math (analysis) a long way into applied math. This notion does of course not make category(!). There is a more general notion of " A - B - measurable functions" that covers what is currently in the article (IMHO: f^{-1}{G) \in A for every G \in B). 90.180.192.165 ( talk) 17:09, 27 November 2012 (UTC)
I have lately been
working on trying to make the sections of
this article pertaining to
measures of infinite unions of measurable sets and
measures of infinite intersections of measurable sets because reading these sections made me feel that they needed some improvements. What does everyone think of my
work so far?
RandomDSdevel (
talk) 22:22, 31 March 2013 (UTC)
The comment(s) below were originally left at Talk:Measure (mathematics)/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.
Delisted GA, needs history, context, simpler explanation. Salix alba ( talk) 20:08, 29 September 2006 (UTC) |
Last edited at 13:26, 15 April 2007 (UTC). Substituted at 02:19, 5 May 2016 (UTC)
So a psych/stat researcher named Stevens( http://www.academic.cmru.ac.th/phraisin/au/prasit/stevens/Stevens_Measurement.pdf) established four types of data and the associated scales that can be used to measure attributes levels of Measurement. How does this relate to measure theory? Is this an application or a coincidental name? Mrdthree ( talk) 21:38, 26 May 2016 (UTC)
Mrdthree ( talk) 22:08, 26 May 2016 (UTC)
The article currently states the composition of measurable functions is itself measurable, which contradicts the Measurable_function page. I believe the composition is only measurable if certain σ-algebras are the same. However, I'm not confident enough to make the edit myself, and would appreciate confirmation from somebody more familiar with all this. 184.186.226.27 ( talk) 23:36, 6 April 2017 (UTC)
This page is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
Edit history was combined with that of Mathematical measure on 2003 Mar 11; the move that broke the history was made on 2002 Oct 26.
This article appears to switch notation about half-way through, from X to S; please see discussion at Talk:Sigma-algebra#Notation. linas 14:11, 25 August 2005 (UTC)
The discussion pages on measure theory -- site to site -- has formed a loop with no information!
Hey, everyone, let's post an example of a non-measurabe set! (unless I missed where it was discussed on Wikipedia...)
Sorry, forgot to sign in -- MathStatWoman anonymous post on 22 dec 2005
I think the non-measureable set term in the section of counterexamples should be emphasize to Lebesgue non-measurable sets ... e.g. Vitali set is not Lebesgue measurable because two properties of translational invariance and countably additivity are inconsistency. The Vitali set may be measurable for other measures that does not requite both two properties .... Jung dalglish 19:12, 3 February 2006 (UTC)
The section Formal definitions currently starts with the following sentence:
The section then continues to define countably additive measures. Do mathematicians always mean countably additive measures when they refer to measures without further qualifications? If yes, this should be stated early on. As the article stands now, the unqualified notion of a measure is never formally defined. (At my first reading of the section I was always expecting a sentence starting with "A measure is then constructed from a countably additive measure by..." or similar.) — Tobias Bergemann 16:11, 16 January 2006 (UTC)
Right now, the material at σ-finite measure seems to be a verbatim copy of the material in the corresponding section of this article. I think splitting off sections is a good idea only when an article gets too long. Thus when some analyst comes here and writes us a book on σ-finiteness, we should split it off, but until that day, we should keep all our articles intact. Therefore I propose changing it to a redirect. I request your comments. - lethe talk + 21:09, 11 March 2006 (UTC)
It is rough for math neophytes to look at formulas first thing off, could it be possible to give more information on these formula... if possible. For the rest, it seems good. Lincher 15:20, 2 June 2006 (UTC)
Should a measure be defined on a semi-ring, then using Carathéodory's extension theorem show that the measure can be extended? — Preceding unsigned comment added by Mikemtha ( talk • contribs) 23:01, 24 October 2006 (UTC)
I changed the section heading for Counterexamples to Non-Measurable Sets and added a 'main article' link to that article (Which, by the way, I'm not a fan of but...) Zero sharp 21:46, 3 November 2006 (UTC)
The Opening says:
In mathematics, a measure is a function that assigns a number, e.g., a "size", "volume", or "probability", to subsets of a given set. The concept has developed in connection with a desire to carry out integration over arbitrary sets rather than on an interval as traditionally done, and is important in mathematical analysis and probability theory.
The introduction is meant to be informal, and I think it does the job well. It gives the idea that each set is mapped to a number. Further details and a more formal definition is supplied below in the text. Oleg Alexandrov ( talk) 02:43, 3 August 2007 (UTC)
I believe the recent changes to the intro made it too complicated and confusing. The first several sentences of an article are very important, and it is important that they are clear and to the point, rather than comprehensive. There is too much repetition now, see sentences 1 and 3. Comments? Oleg Alexandrov ( talk) 02:56, 6 August 2007 (UTC)
Can someone please add a section on the practical applications of measure theory? My interviews with a broad range of scientists suggests that measure theory has a zero measure of contribution to any sort of applied science. —Preceding unsigned comment added by 24.226.30.183 ( talk) 05:16, 18 January 2008 (UTC)
This article is pretty much nonsense at the moment. Being a measure theorist, I am surprised how this article got to GA in the first place (but now it is demoted). The point is that many of the important topics in measure theory are non included not to mention that the lede is not up to par (politely speaking). I will start a rewrite now. PST
Why μ(Ø) = 0 appears as part of the definition?! It follows from additivity, doesn't it? Maybe it should be moved down as note? Vasili Galka ( talk) 17:32, 24 June 2009 (UTC)
Actually it's not necessarily redundant. It depends on the meaning of 'countable collection'. Some use 'countable' to mean 'infinitely countable', and σ-additivity usually does refer to the infinite case. In such case, the above proof of the second axiom from the third doesn't pass, and in fact one has to rely on the second to deduce finite additivity from σ-additivity. bungalo ( talk) 21:09, 27 June 2012 (UTC)
User:Finell on 21 July 2009 required inline citations. However, "Editors making a challenge should have reason to believe the material is contentious, false, or otherwise inappropriate", according to Wikipedia:When to cite#Challenging another user's edits. Is it the case here? Could Finell be more specific, pointing to a problem? Boris Tsirelson ( talk) 19:08, 18 August 2009 (UTC)
The definition claims that Σ is a σ-algebra, that μ is a function on Σ, and that but if you click on the link to σ-algebra you'll find the first point in the definition of a σ-algebra that it must be non-empty. So shouldn't be in the domain of , making the second point in the definition apparent nonsense. Would knowledgeable someone please clear this up. Pulu ( talk) 23:23, 8 October 2010 (UTC)
I just read through the lead on this article and I think it stands as a model of how to make a comprehensible lead for a potentially very technical subject. Good work! Benwing ( talk) 05:09, 21 October 2010 (UTC)
1. There is not a single citation.
2. In particular, re: "a mysterious function called the "mean width", a misnomer." Provide citations for who used the term and who stated it is a misnomer. Also, is this good mathematical writing? Michael P. Barnett ( talk) 21:14, 3 May 2011 (UTC)
The pair is called a measurable space -- is undefined. — Preceding unsigned comment added by 193.219.42.53 ( talk) 10:59, 19 November 2012 (UTC)
Contrary to what is stated in the article, "measurable function" is defined to be a function that has f^{-1}(G) measurable for every open (or closed) set G. This meaning of the notion is the usual one from pure math (analysis) a long way into applied math. This notion does of course not make category(!). There is a more general notion of " A - B - measurable functions" that covers what is currently in the article (IMHO: f^{-1}{G) \in A for every G \in B). 90.180.192.165 ( talk) 17:09, 27 November 2012 (UTC)
I have lately been
working on trying to make the sections of
this article pertaining to
measures of infinite unions of measurable sets and
measures of infinite intersections of measurable sets because reading these sections made me feel that they needed some improvements. What does everyone think of my
work so far?
RandomDSdevel (
talk) 22:22, 31 March 2013 (UTC)
The comment(s) below were originally left at Talk:Measure (mathematics)/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.
Delisted GA, needs history, context, simpler explanation. Salix alba ( talk) 20:08, 29 September 2006 (UTC) |
Last edited at 13:26, 15 April 2007 (UTC). Substituted at 02:19, 5 May 2016 (UTC)
So a psych/stat researcher named Stevens( http://www.academic.cmru.ac.th/phraisin/au/prasit/stevens/Stevens_Measurement.pdf) established four types of data and the associated scales that can be used to measure attributes levels of Measurement. How does this relate to measure theory? Is this an application or a coincidental name? Mrdthree ( talk) 21:38, 26 May 2016 (UTC)
Mrdthree ( talk) 22:08, 26 May 2016 (UTC)
The article currently states the composition of measurable functions is itself measurable, which contradicts the Measurable_function page. I believe the composition is only measurable if certain σ-algebras are the same. However, I'm not confident enough to make the edit myself, and would appreciate confirmation from somebody more familiar with all this. 184.186.226.27 ( talk) 23:36, 6 April 2017 (UTC)