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Math Help - Uniform Convergence

  1. #1
    Junior Member tedii's Avatar
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    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].
    Last edited by tedii; February 11th 2010 at 07:57 PM.
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  2. #2
    Junior Member tedii's Avatar
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    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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