Timeline for Do regular conditional distributions almost surely assign trivial measure to all members of the conditioning $\sigma$-algebra?
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| Aug 12, 2014 at 0:36 | comment | added | Julian Newman | Incidentally, the proof given for the "invariance" part seems a little overkill; see math.nus.edu.sg/~matsr/ProbII/Lec10.pdf for quite a direct proof. | |
| Aug 12, 2014 at 0:33 | comment | added | Julian Newman | Thank you for your reply. I am aware that the answer is "yes" when $\mathcal{E}$ is countably generated (see the first comment below the question). As for the ergodic decomposition: the reference you gave uses the fact that $\mathcal{E}$ is countably generated $\bmod P$ specifically to prove the "invariance" part [the easy part], not the "ergodicity" part [the part that I'm concerned about]. For the "ergodicity" part, the reference you gave still uses Birkhoff's ergodic theorem. | |
| Aug 11, 2014 at 22:25 | history | answered | Yuri Bakhtin | CC BY-SA 3.0 |