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Questions about abstract measure and Lebesgue integral theory. Also concerns such properties as measurability of maps and sets.

10 votes
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Is there a measure on $[0,1]$ that is 0 on meagre sets and 1 on co-meagre sets

I'm curious if there is a finite measure on the $\sigma$-algebra of subsets of $[0,1]$ with the Property of Baire, whose null sets are exactly the meagre sets. I'd also be interested how "nice" such …
Tom Bouley's user avatar