Problem: Suppose that $\left\{ f_n \right\} $ is a sequence of continuous functions defined on $[a,b]$ such that for all $x\in [a,b]$ and $n\in \mathbb{N} $ we have $f_n(x) \geq f_{n+1}(x)$. If $\left\{ f_n \right\} $ converges to a continuous function $f$ pointwise on $[a,b]$, then prove that the convergence is uniform. This is known as Dini's Theorem.
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