Let ([0,1], L, m) be a Lebesgue measure space, and let A be a nonempty measurable subset of [0,1]. Let {E}-1 = [0,1] be a countable disjoint collection of Lebesgue measurable sets. Let f: [0,1] → (0,1] be a measurable function. Show that for every e > 0, there is a natural number №e and a set C such that m(C) < € and < f(x) ≤ for all x € Ce. 1 NE+1 NE

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