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Problem 1. Let {En}n∞=1 be a sequence of nonempty (Lebesgue) measurable subsets of [0, 1] satisfying...

Problem 1. Let {En}n∞=1 be a sequence of nonempty (Lebesgue) measurable subsets of [0, 1] satisfying

limn→∞m(En) = 1.

Show that for each ε ∈ [0, 1) there exists a subsequence {Enk }k∞=1 of {En}n∞=1 such that m(∩k∞=1Enk) ≥ ε

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