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

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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 1 (165.45 KiB) Viewed 47 times

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 N and a set C such that - for all x E CE. 1 1 m(C) < € and NE+1 NE <f(x) ≤