Talk:Standard probability space

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I'm not familiar with the idea of "countable probability spaces" being "standard". Is there any reference to this idea in a text book?

The definition is given according to the three articles cited (and many others). About textbooks, I'll try to find something appropriate. Boris Tsirelson (talk) 08:51, 30 January 2008 (UTC)

Not a text book, but an encyclopedia is found. Namely: Encyclopedic Dictionary of Mathematics (second edition) by the Mathematical Society of Japan, edited by Kiyosi Ito, The MIT Press. See Volume 1, article 136 "Ergodic Theory", item A "General remarks" on page 531:

A Lebesgue measure space with a finite measure (σ-finite measure) is a measure space that is measure-theoretically isomorphic to a bounded interval (to the real line) with the usual Lebesgue measure, possibly together with an at most countable number of atoms.

Boris Tsirelson (talk) 10:16, 30 January 2008 (UTC)

An appropriate textbook is found, and added to the article as [4]. In the book, see Item (a) on page 65 (just after the proof of Theorem 2.4.1). Boris Tsirelson (talk) 19:30, 30 January 2008 (UTC)