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Let f n {\displaystyle f_{n}} be a sequence of functions defined on a closed interval [ a , b ] {\displaystyle [a,b]} of the real line. If f n {\displaystyle f_{n}} is uniformly bounded and equicontinuous then it contains a subsequence that converges uniformly.
![{\displaystyle [a,b]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9c4b788fc5c637e26ee98b45f89a5c08c85f7935)