Let $U \subset \mathbb{R}^d$ be a bounded set of Lebesgue measure zero, $\mu(U) = 0$. Can we find an open set $V$ containing $U$ such that $\mu(V) < \epsilon$ for any $\epsilon > 0$? Seems intuitive, but I'm not sure how to prove it.
2026-04-17 22:15:19.1776464119
Small open set containing a set of measure zero
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As Robert Israel pointed out in the comment, it is implied by regularity of Lebesgue measure. Although the Wikipedia page states it only for the real line, it holds for $\mathbb{R}^n$.