The Kolmogorov-Riesz compactness theorem

Details The Kolmogorov-Riesz compactness theorem The Kolmogorov-Riesz compactness theorem

2009-06-26

arxiv.org/abs/0906.4883v2

Expositiones Mathematicae 28 (2010) 385-394

Mathematics

Classical Analysis and ODEs

This version is lightly revised in response to referee comments. The paper will appear in Expositiones Mathematicae

Scientific paper

10.1016/j.exmath.2010.03.001

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.

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