# Uniform Convergence

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• February 11th 2010, 06:20 PM
tedii
Uniform Convergence
I have been staring at this problem all day and I can't figure how to even begin to form subsequence. Can someone give me a jump start?

Let $\{f_n\}$ be a uniformly bounded sequence of functions which are Riemann-integrable on [a, b], and put

$F_n(x) = \int_a^x f_n(x), dt (a \leq x \leq b).$

Prove that there exists a subsequence $\{F_{n_k}\}$ which converges uniformly on [a, b].
• February 11th 2010, 07:43 PM
tedii
The problem is from Blue Rudin chapter 7 problem 18. Also I believe I am supposed to follow a format similar to the proof of Theorem 7.23. I hope this helps.

Thank you for any advice.
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