Talk:Standard Borel space

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)