Trying to understand corollary of the Sanov's theorem and the problem basically reduces finding such set. My first idea was Cantor set, but turns out its interior is empty
2026-04-25 01:28:36.1777080516
Does there exist an interval, or more generally a set with non-empty interior, whose Lebesgue measure is 0?
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Remember that whenever $A \subset B$ it holds that $\mu(A)\leq\mu(B)$. Now what can you say about the Lebesgue measure of an open set?