Let $G$ be compact (and Hausdorff) group, $\mu$ be Haar measure on $G$. Is it always true that $(G,\mu)$ is a standard probability space (Lebesgue-Rokhlin space)? It is so if (a priori not iff) the topology of $G$ is metrizable, but this is probably not necessary.
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asked May 11, 2011 at 17:39
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4$\begingroup$ Well, some silly counter-examples: A finite group. Or $\{0,1\}^I$ for some very, very large set $I$. $\endgroup$– Matthew DawsCommented May 11, 2011 at 19:10
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$\begingroup$ well, finite does not count, I had to mention it the second example is ok, thank you $\endgroup$– Fedor PetrovCommented May 11, 2011 at 19:54
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