Consider the family F := {F(x) = X 1. f(t)dt f = C(0, ) and ||f||...

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Consider the family F := {F(x) = X 1.² f(t)dt f = C(0, ∞) and ||f||∞ ≤ 1}. Show that every sequence (fn)nz1 C F has a subsequence that converges uniformly on [0, k] for every k > 0. Hint: use the function Mx := supƒer |ƒ(x)]. Consider the family F := {F(x) = X 1.² f(t)dt f = C(0, ∞) and ||f||∞ ≤ 1}. Show that every sequence (fn)nz1 C F has a subsequence that converges uniformly on [0, k] for every k > 0. Hint: use the function Mx := supƒer |ƒ(x)].

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Solution To show that every sequence fnn1 CF has a subsequence that converges uniformly on 0 k for e... View the full answer