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