Suppose $\epsilon \in (0, 1)$ and $m$ is Lebesgue measure. What is a measurable set $E \subset [0, 1]$ such that the closure of $E$ is $[0, 1]$ and $m(E) = \epsilon$?
2026-04-03 22:40:35.1775256035
What is a measurable set $E \subset [0, 1]$ such that the closure of $E$ is $[0, 1]$ and $m(E) = \epsilon$?
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HINT: You can add $\Bbb Q\cap[0,1]$ to any measurable subset of $[0,1]$ without changing its measure.