The Kolmogorov-Riesz compactness theorem
arXiv:0906.4883 · doi:10.1016/j.exmath.2010.03.001
Abstract
We show that the Arzela-Ascoli theorem and Kolmogorov compactness theorem both are consequences of a simple lemma on compactness in metric spaces. Their relation to Helly's theorem is discussed. The paper contains a detailed discussion on the historical background of the Kolmogorov compactness theorem.
This version is lightly revised in response to referee comments. The paper will appear in Expositiones Mathematicae
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