Let In be integrable and supn J fndu < 0. If fn T f, prove that f is integrable and f fndu S fdu. Hints: a) 0 < (fn - fi) ↑ (f – fi). Apply the MCT. b) Let g = f- fiı. Then gdu = lim, S(fn- fi)du < sup, S(fn- f1)du. Show this implies g is integrable. c) Then g+ fi = f is integrable. %3D

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