Let $\epsilon \in (0, 1)$, let $m$ be Lebesgue measure, and suppose $A$ is a Borel measurable subset of $\mathbb{R}$. If$$m(A \cap I) \le (1 - \epsilon)m(I)$$for every interval $I$, then does it follow that $m(A) = 0$?
2026-04-24 10:12:04.1777025524
If $m(A \cap I) \le (1 - \epsilon)m(I)$ for every interval $I$, then $m(A) = 0$?
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