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Problem 2. Prove that if a measurable subset E ⊂ [0, 1] satisfies m(E ∩ I)...

Problem 2. Prove that if a measurable subset E ⊂ [0, 1] satisfies m(E ∩ I) ≥ αm(I), for some α > 0 and all intervals I ⊂ [0, 1], then m(E) = 1. Hint: A corollary about points of density proved in the class, may help.

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