Vitali Type Convergence Theorems for Banach Space Valued Integrals

被引：6
|
作者：
Balcerzak, Marek [1 ]
Musia, Kazimierz [2 ]
机构：
[1] Lodz Univ Technol, Inst Math, PL-93005 Lodz, Poland
[2] Univ Wroclaw, Inst Math, PL-50384 Wroclaw, Poland
来源：
ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2013年 / 29卷 / 11期
关键词：
Convergence theorems for integrals; Pettis integral; scalar equi-convergence in measure; I-convergence; STATISTICAL CONVERGENCE; SEQUENCES;
D O I：
10.1007/s10114-013-2578-1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let (Omega, Sigma, mu) be a complete probability space and let X be a Banach space. We introduce the notion of scalar equi-convergence in measure which being applied to sequences of Pettis integrable functions generates a new convergence theorem. We also obtain a Vitali type I-convergence theorem for Pettis integrals where I is an ideal on N.
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页码：2027 / 2036
页数：10
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