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    Real Analysis : Convergence and Monotone Increasing and Continuous Functions

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    Prove that if for each natural number, n, the function f_n on I = [0,1] ---> the reals is monotone increasing and if f(x)=limit as n--->infinity of f_n(x) is continuous on I, then the convergence is uniform on I.

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    Solution Summary

    Convergence, monotone increasing and continuous functions are investigated. The solution is detailed and well presented.