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Uniform Convergence of a Sequence of Functions

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September 30th, 2022

Prove the following theorem.

Let f1,f2,f3…. be continuous functions on a closed bounded interval [a,b] . Then fn—>f uniformly on [a,b] if and only if
fn(x)–>f(x) for every xn-->x such that xn,x E[a,b] .

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