If $A \subset \Bbb{R}$ is Lebesgue measurable.($m$ is Lebesgue measure) and for every compact $K \subset A$, $m(K)=0$; is it true that $m(A)=0$?
2026-04-06 15:56:53.1775491013
Is a Lebesgue measurable subset a null set if each compact subset is a nullset?
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Yes, $m(A) = 0$, given your hypothesis. This is a direct consequence of the inner regularity of Lebesgue measure, as David pointed out, which states that $$ m(A) = \sup\{ m(K) : K \subset A, K \textrm{ compact} \}. $$