The Kolmogorov-Riesz compactness theorem

被引：155

作者：

Hanche-Olsen, Harald ^{[1
]}

Holden, Helge ^{[1
,2
]}

机构：

[1] Norwegian Univ Sci & Technol, Dept Math Sci, NO-7491 Trondheim, Norway

[2] Univ Oslo, Ctr Math Applicat, NO-0316 Oslo, Norway

来源：

EXPOSITIONES MATHEMATICAE | 2010年 / 28卷 / 04期

关键词：

Kolmogorov-Riesz compactness theorem; Compactness in L-P;

D O I：

10.1016/j.exmath.2010.03.001

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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. (C) 2010 Elsevier GmbH. All rights reserved.

引用

页码：385 / 394

页数：10

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