Question is in the title. I've tried examples to show there is such a $D$ but not had any luck, and a proof that there is no such $D$ doesn't seem to go anywhere.
2026-03-25 20:18:14.1774469894
Does there exist a Lebesgue measurable set $[0,1] \subset D$ such that $D \neq [0,1]$ and $\lambda ^{*} (D) = 1$?
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