2. (10 points) Let {fn} be a uniformly bounded sequence of functions which are Riemann-integrable on...

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2. (10 points) Let {fn} be a uniformly bounded sequence of functions which are Riemann-integrable on [a, b], and define x Fn(x) = f* fn(t) dt, a x b. Prove that there exists a subsequence {Fnk} which converges uniformly on [a, b]. 2. (10 points) Let {fn} be a uniformly bounded sequence of functions which are Riemann-integrable on [a, b], and define x Fn(x) = f* fn(t) dt, a x b. Prove that there exists a subsequence {Fnk} which converges uniformly on [a, b].