The Kolmogorov-Riesz compactness theorem
Classical Analysis and ODEs
2010-10-26 v2 Functional Analysis
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.
Cite
@article{arxiv.0906.4883,
title = {The Kolmogorov-Riesz compactness theorem},
author = {Harald Hanche-Olsen and Helge Holden},
journal= {arXiv preprint arXiv:0906.4883},
year = {2010}
}
Comments
This version is lightly revised in response to referee comments. The paper will appear in Expositiones Mathematicae