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The Kolmogorov-Riesz compactness theorem

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.

preprint2010arXivOpen access
Harald Hanche-OlsenHelge Holden
math.FAmath.CA
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Harald Hanche-OlsenHelge Holden

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