Suppose $\epsilon \in (0, 1)$ and $m$ is Lebesgue measure. Find a measurable set $E \subset [0, 1]$ such that the closure of $E$ is $[0, 1]$ and $m(E) = \epsilon$.
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2026-04-08 15:32:02.1775662322
Construction a measure in $[0,1]$
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Hint: What the closure of $\mathbb Q \cap (0,1)$, and what is the measure?