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

9 votes
3 answers
395 views

Countable shifts of closed positive sets

Let $\mu$ be the Lebesgue measure, and $+$ be addition modulo $1$ in the interval $[0,1)$. Question1: Is there a closed set $C\subset [0,1)$ of positive measure such that for any countable set $D\sub …