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Talk:Σ-finite measure

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Requested move

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.

sigma-finite \mu

@Mennucc Regarding your recent edit. Page 41 of Rudin does state that μ < inf {\displaystyle \mu <\inf } is countably additive. Wouldn't that imply it being σ {\displaystyle \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)
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