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.

引用

页码：2027 / 2036

页数：10

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