Let {Sn} be a sequence of real-valued functions on [0, 1] defined by fo = f e C[0,1] and fn is an antiderivative of fn-1

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Let Sn Be A Sequence Of Real Valued Functions On 0 1 Defined By Fo F E C 0 1 And Fn Is An Antiderivative Of Fn 1 1 (29.42 KiB) Viewed 43 times

Let {Sn} be a sequence of real-valued functions on [0, 1] defined by fo = f e C[0,1] and fn is an antiderivative of fn-1. Suppose that for each € [0, 1] there is n e N for which fn(x) = 0. Prove that f = 0.