Question: Exercise 5.1.3:Letf : [a, b] R be a bounded function. Suppose that there exists a sequence of partitions { P k } of [a, b]

Exercise 5.1.3:Letf : [a, b] R be a bounded function. Suppose that there exists a sequence of

partitions {Pk } of [a, b] such that

limk(U(Pk,f)L(Pk,f))=0 .

Show thatfis Riemann integrable and that

abf = limkU(Pk,f)=limkL(Pk,f) .

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