Talk:Σ-finite measure

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 Field:  Analysis

Requested move[edit]

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[edit]

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.