Are dense subsets almost nothing or almost everything? – math.stackexchange.com

Are dense subsets almost nothing or almost everything? – math.stackexchange.com

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Dense subsets of $[0,1]$ I know have Lebesgue measure $0$ or $1$, but, is there any dense, uniform subset of $[0,1]$ with meausre $1/2$? What I mean with uniform: a subset $A$ of $[0,1]$ is uniform ...

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