Let (fn) C[0, 1] be such that there exists M> 0 such that ||fn|| M, for...

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Let (fn) C[0, 1] be such that there exists M> 0 such that ||fn|| M, for all n N. Define Fn(x) = f* fn(t) dt. 0 Show that Fn has a uniformly convergent subsequence. Let (fn) C[0, 1] be such that there exists M> 0 such that ||fn|| M, for all n N. Define Fn(x) = f* fn(t) dt. 0 Show that Fn has a uniformly convergent subsequence.

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