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Apr 13, 2017 at 12:58 history edited CommunityBot
replaced http://mathoverflow.net/ with https://mathoverflow.net/
Aug 13, 2014 at 20:47 vote accept Julian Newman
Aug 13, 2014 at 20:46 answer added Julian Newman timeline score: 4
Aug 12, 2014 at 2:57 history edited Julian Newman CC BY-SA 3.0
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Aug 12, 2014 at 2:39 history edited Julian Newman CC BY-SA 3.0
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Aug 12, 2014 at 2:07 history edited Julian Newman CC BY-SA 3.0
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Aug 11, 2014 at 22:25 answer added Yuri Bakhtin timeline score: 1
Aug 11, 2014 at 22:21 answer added Algernon timeline score: 2
Aug 11, 2014 at 16:09 comment added Julian Newman I've "revamped" the question to take into account the papers you've informed me of. Thank you very much for your help.
Aug 11, 2014 at 16:08 history edited Julian Newman CC BY-SA 3.0
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Aug 11, 2014 at 14:56 comment added Julian Newman Thanks. I think this answers my second question, but not my first (unless I read the papers too quickly).
Aug 11, 2014 at 14:30 history edited Julian Newman CC BY-SA 3.0
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Aug 11, 2014 at 13:06 comment added Jochen Wengenroth I think that this projecteuclid.org/euclid.aop/1015345764 answers your question.
Aug 11, 2014 at 12:27 comment added Jochen Wengenroth I have deleted my answer (which in fact did not answer the question). Meanwhile, I think that the answer to you question is NO. It might be helpful to study (more carefully than I did) the following projecteuclid.org/…
Aug 11, 2014 at 12:15 comment added Julian Newman I realise (thanks to Jochen Wengenroth) that I should perhaps emphasise: In the case that $\mathcal{E}$ is countably generated, the answer to both questions is yes, since clearly, for each $E \in \mathcal{E}$, $\rho_x^\mathcal{E}(E)=\mathbf{1}_E(x)$ a.e. (and then the $\pi$-$\lambda$ theorem gives the result, by considering a countable $\pi$-system generating $\mathcal{E}$). The difficulty in my questions is specifically due to the fact that I haven't assumed $\mathcal{E}$ to be countably generated. (I've only assumed $\Sigma$ to be countably generated, since $\Sigma$ is standard.)
Aug 11, 2014 at 2:47 history asked Julian Newman CC BY-SA 3.0