Talk:Σ-finite measure

Requested move

 * The correct title of σ-finite measure can now be achieved by moving the article to Σ-finite measure (which is currently a redirect) and using the template. --Zundark (talk) 12:48, 11 October 2008 (UTC)
 * I did the move. It needed histmerge. Anthony Appleyard (talk) 13:51, 11 October 2008 (UTC)

Why no redirect from sigma-finite measure? Most keyboards can't type Σ in the search box. Thenub314 (talk) 15:08, 15 October 2008 (UTC)


 * There is a redirect from sigma-finite measure. Anthony Appleyard created it when he did the move. --Zundark (talk) 15:21, 15 October 2008 (UTC)

σ-finiteness of measures on rings
The article "Carathéodory's extension theorem" links here in the "Statement of the theorem" section, but the (pre)measure μ in question is defined on a ring, not a σ-algebra. Hence, the definition provided here is not general enough.

Borrowing from "A basic course in measure and probability: theory for applications", by Ross Leadbetter, Stamatis Cambanis and Vladas Pipiras (page 22), I would suggest the following definition:

μ is σ-finite if for every E in its domain, there is a sequence (E_n) of sets in its domain such that E is contained in the union of the E_n and μ(E_n) is finite for every n.

TLE
whrite at least 10 measure equivalent in your TLE notebook 122.54.158.177 (talk) 01:35, 9 December 2021 (UTC)

sigma-finite \mu
@Mennucc Regarding your recent edit. Page 41 of Rudin does state that $$\mu < \inf$$ is countably additive. Wouldn't that imply it being $$\sigma$$-finite? Roffaduft (talk) 03:18, 4 April 2024 (UTC)


 * I do not understand what you mean by " μ < inf is countably additive". Also look in Rudin at exercise 16 at the end of chap 3. Mennucc (talk) 17:41, 17 April 2024 (UTC)