Mean Convergence Theorems and Weak Laws of Large Numbers for Arrays of Measurable Operators under Some Conditions of Uniform Integrability

被引：0
作者：
Nguyen Van Quang
Do The Son
Tien-Chung Hu
Nguyen Van Huan
机构：
[1] Vinh University,Department of Mathematics
[2] Industrial University of Ho Chi Minh City,Faculty of Fundamental Science
[3] Tsing Hua University,Department of Mathematics
[4] Institute for Computational Science and Technology (ICST),Department of Mathematics and Applications
[5] Saigon University,undefined
来源：
Lobachevskii Journal of Mathematics | 2019年 / 40卷
关键词：
mean convergence theorems; weak laws of large numbers; arrays of measurable operators; von Neumann algebra; noncommutative probability; rowwise pairwise independent; uniform integrability;
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学科分类号：
摘要：
In this paper, we introduce the notions of uniform integrability in the Cesàro sense, h-integrability with respect to the array of constants {ani}, and h-integrability with exponent r for an array of measurable operators. Then, we establish some mean convergence theorems and weak laws of large numbers for arrays of measurable operators under some conditions related to these notions.
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页码：1218 / 1229
页数：11
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