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Real Analysis : Convergence and Monotone Increasing and Continuous Functions

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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Convergence, Monotone Increasing and Continuous Functions are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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