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Let A denote Lebesgue measure on R. (a) Let f(x) = 1/x. Prove that [0,1] f d (b) Let f(x)=1/(1+x). (c) Let f(x) =

Let A denote Lebesgue measure on R. (a) Let f(x) = 1/x. Prove that [0,1] f d (b) Let f(x)=1/(1+x). (c) Let f(x) = (sinx)/x. Show that the integral (0,) f d is not defined but limt (0,t) f d exists in R. = Prove that fRf d = .

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