- Let f: [0,1] -> [0,00) be Lebesgue measurable. For n € N, define fr 9n 1 + fn (a) Explain why gn(t) dt exists and is finite for all n. (b) Prove that lim gn (t) dt exists and find an expression for it. Make sure to state which major Theorem are you using in your proof. 72-00

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