EDB — 1K2

[1K2]Prerequisites:[1HR]↺↻,[0VC]↺↻, [1JG]↺↻.[3]↺↻.Difficulty:*.

Let now \(I⊆ ℝ\) be a closed and bounded interval. Let \(f_ n:I→ℝ\) continuous functions, and suppose that the sequence \((f_ n)\) is equicontinuous and bounded (i.e. \(\sup _ n \| f_ n\| _∞{\lt}∞\)). Show that there is a subsequence \(f_{n_ k}\) that converges uniformly.