Question: F.(a) Let Fbe a subset ofC[0,1] that is closed, bounded, and equicontinuous. Prove that thereis a function ginF such that01g(x)dx01f(x)dx, for all ,finF(b) Construct a

F.(a) Let Fbe a subset ofC[0,1] that is closed, bounded, and equicontinuous. Prove that thereis a function ginF such that01g(x)dx01f(x)dx, for all ,finF(b) Construct a closed bounded subset FofC[0,1] for which the conclusion of the previousproblem is false.

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