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    Sequences and Uniform Convergence

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    Let {fn} infinity-->n-1 be a sequence of continuous real-valued functions that converges uniformly on the closed bounded interval [a, b]. For each nЄ I let
    Fn(x) = &#8747; x--> a fn(t)dt a<x<b
    Show that {fn} infinity-->n-1 converges uniformly on [a,b]. (Hint: Use 9.2F)

    Theorem 9.2F;
    Let be a sequence of real-valued functions on a set E. Then is uniformly convergent on E ( to some function) if and only if given there exists such that
    ---

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    https://brainmass.com/math/real-analysis/sequences-uniform-convergence-58107

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    Problem:

    Let be a sequence of continuous real-valued functions that converges uniformly on the closed bounded interval [a, b]. For each let

    Show that converges ...

    Solution Summary

    Sequences and Uniform Convergence are investigated. The solution is detailed and well presented.

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