p-convergence in measure of a sequence of measurable functions and corresponding minimal elements of c0

被引：3

作者：

Papanastassiou, Nikolaos ^{[1
]}

Papachristodoulos, Christos ^{[1
]}

机构：

[1] Univ Athens, Dept Math, Athens 15785, Greece

来源：

POSITIVITY | 2009年 / 13卷 / 01期

关键词：

p-convergence in measure; upper sequence; lower sequence; minimal zero sequence;

D O I：

10.1007/s11117-008-2185-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We characterize convergence in measure of a sequence (f(n))(n) of measurable functions to a measurable function f by elements of c(0), which express the quality of convergence of (f(n))(n) to f. This characterization motivates the introduction of a new notion of convergence, called "p-convergence in measure" (p > 0), which is stronger than convergence in measure. We prove the existence of "minimal" elements in c(0) which characterize the convergence in measure of (f(n))(n) to f.

引用

页码：243 / 253

页数：11

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