Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Dear Andreas Blass: The example you presented may be seen as a sequence $[f(T^n(x))]_n$, where $f: X \to R$ and $T: X \to X$ are measurable (are even better than that). For those $f$ and $T$, the Birkhoff (arithmetical) average of $f$ [that is, $f_n(x)=1/n \sum_{j=1}^{n-1} f (T^j(x))$] converges for Lebesgue almost every $x$. Do you know an example (where measurability, in spite of $f$ and $T$ being measurable, is lost through a non-principal ultrafilter limit) such that the sequence $(f_n)_n$ is a Birkhoff average?

share|improve this question
    
@DavideGiraudo Most likely this one. –  Harald Hanche-Olsen Jan 21 '13 at 15:34
    
Here is the link with Andreas Blass' example: math.stackexchange.com/questions/275365/… –  user59396 Jan 23 '13 at 17:38
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.