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arXiv · 0906.4883

The Kolmogorov-Riesz compactness theorem

Harald Hanche-Olsen·Helge Holden
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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.

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BibTeXRIS

Harald Hanche-Olsen, Helge Holden. 2010-01-04. The Kolmogorov-Riesz compactness theorem. https://doi.org/10.1016/j.exmath.2010.03.001

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