3
$\begingroup$

In this paper: 'Borel structures for Function spaces' by Robert Aumann,

http://projecteuclid.org/euclid.ijm/1255631584

Aumann claims that when X and Y are metric spaces (among other things), the Baire classes and Banach classes coincide, I've been looking all over and can't find a reference or proof, I need to know if the result can be extended to METRIZABLE spaces (that is, if the Baire classes and Banach classes coincide for metrizable spaces too), I desperately need this to be true for a proof I'm working on, it's like the last step in my proof, so I was wondering if anyone knows this or can point me in the right direction? In Aumann's paper There's a reference to this paper: 'Über analytisch darstellbare Operationen in abstrakten Räumen' by Banach, but it's in german and I don't speak it and as far as I know there's no translation to english.

$\endgroup$
  • 2
    $\begingroup$ The best thing you can do that I'm aware of is the case where $X$ and $Y$ are metrizable and $Y$ is in addition separable. A proof can be found in Section 24 of Kechris, Classical Descriptive Set Theory, Theorem 24.3. This proof makes essential use of separability of $Y$. $\endgroup$ – Theo Buehler Jun 23 '11 at 6:20
  • 2
    $\begingroup$ And, since there is no answer, the system will keep re-posting to the front page from time to time (as it did today). $\endgroup$ – Gerald Edgar Feb 25 '14 at 17:38

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.