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Talk:Standard Borel space

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Question about relation to standard probability space

In the entry, it is stated the following:

Let $(X,\mathcal A)$ be a standard Borel space and $\mu:\mathcal A\to[0,1]$ a probability measure. Then $(X,\mathcal A,\mu)$ is a standard probability space.

However, the definition given in the entry standard probability space states that the measure should be completed. Although I understand that different authors can make use of slightly different definitions, it would be better for this site to be consistent. So, maybe the property should be:


Let $(X,\mathcal A)$ be a standard Borel space and $\mu:\mathcal A\to[0,1]$ a probability measure. Then the completion of $(X,\mathcal A,\mu)$ is a standard probability space.

Pom (talk) 22:31, 26 September 2013 (CEST)

Yes, indeed! It was my careless mistake. Many thanks for pointing it. --Boris Tsirelson (talk) 07:48, 27 September 2013 (CEST)
Thank you very much for this clarification. Pom (talk) 07:53, 27 September 2013 (CEST)
How to Cite This Entry:
Standard Borel space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Standard_Borel_space&oldid=30552