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
Posted: Tue Sep 07, 2021 7:34 am
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.