Timeline for Do the Birkhoff averages of a measurable stationary homogeneous Markov process in continuous time "converge to the right limit"?

10 events

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Jul 31 at 17:10	comment	added	No-one		The only thing I know for sure is that $L:Z\to \mathbb{R}$ can never be a measurable map with respect to the product $\sigma$-algebra on $Z$, since if it were then it would be $L((x_t)_{t\in[0,\infty)})=L((x_{t_k})_{k\in \mathbb{N}})$ for some sequence $(t_k)$, which is clearly not the case since $L$ is independent of the value of $x$ on any fixed sequence of times.
Jul 31 at 17:10	comment	added	No-one		I know it is a very old question but I have just got stuck at exact same point as you. Do you perhaps have an answer after all these years? I've realised you posted a follow up question here, but unfortunately I do not see how to use its answer in the present setting.
Apr 13, 2017 at 12:57	history	edited	CommunityBot		replaced http://mathoverflow.net/ with https://mathoverflow.net/
Jun 27, 2015 at 17:28	history	edited	Julian Newman	CC BY-SA 3.0	Adding clarity.
Jun 27, 2015 at 17:16	history	edited	Julian Newman	CC BY-SA 3.0	Improved overall clarity
Mar 16, 2015 at 1:29	history	edited	Julian Newman	CC BY-SA 3.0	added 51 characters in body
Mar 16, 2015 at 1:17	history	edited	Julian Newman	CC BY-SA 3.0	added 51 characters in body
Mar 10, 2015 at 13:35	history	edited	Julian Newman	CC BY-SA 3.0	Update added
Mar 10, 2015 at 4:02	history	edited	Julian Newman	CC BY-SA 3.0	added 18 characters in body
Mar 10, 2015 at 3:32	history	asked	Julian Newman	CC BY-SA 3.0