p-q-convergence of sequences of measurable functions

被引：1
|
作者：
Papachristodoulos, C. [1 ]
Papanastassiou, N. [1 ]
Wilczynski, W. [2 ]
机构：
[1] Univ Athens, Dept Math, GR-10679 Athens, Greece
[2] Univ Lodz, Dept Math, PL-90131 Lodz, Poland
来源：
TOPOLOGY AND ITS APPLICATIONS | 2011年 / 158卷 / 12期
关键词：
q-complete convergence; p-q-complete convergence;
D O I：
10.1016/j.topol.2011.05.020
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We introduce new types of convergence of sequences of measurable functions stronger than convergence in measure for each pair of positive real numbers p, q and we obtain a classification of convergences in measure. Also in the space M of sequences of measurable functions converging in measure to zero, we introduce in a natural way an equivalence relation similar to, and in the quotient space M = M/similar to a metric, under which M turns to be a complete metric space. (C) 2011 Elsevier B.V. All rights reserved.
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页码：1478 / 1492
页数：15
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