Comments on: Standard Borel Spaces

By: Walt

Walt — Wed, 12 Nov 2008 03:20:28 +0000

You’re right. I forgot “separable”.

By: John Baez

John Baez — Wed, 05 Nov 2008 23:42:05 +0000

Thanks for the Parthasarathy reference! It helped a lot!

By: John Baez

John Baez — Tue, 04 Nov 2008 18:26:46 +0000

By the way, I think you gave the wrong definition of ’standard Borel space’. It’s a set with a σ-algebra which can be realized as the set of Borel sets of a separable complete metric space.

I think this extra word eliminates some pathologically large examples.

By: Walt

Walt — Mon, 22 Sep 2008 20:34:55 +0000

It’s true.

I think the standard reference for the topic is Parthasarathy’s Probability Measures on Metric Spaces.

By: John Baez

John Baez — Mon, 22 Sep 2008 20:04:16 +0000

Yes it’s true, or yes this paper will answer my question?

By: Walt

Walt — Sat, 20 Sep 2008 18:50:34 +0000

Yes.

By: John Baez

John Baez — Sat, 20 Sep 2008 13:39:07 +0000

Yay! Not too late for the paper I’m writing with Derek Wise, Aristide Baratin and Laurent Freidel… the one that made us learn about Polish spaces.

If you take a Polish space and think of it as a set with a sigma-algebra of subsets, is this the same as a standard Borel space? I thought I convinced myself that this was true.

Maybe this paper will answer that question.