A NEW VERSION OF UNIFORM INTEGRABILITY VIA POWER SERIES SUMMABILITY METHODS*

被引：4

作者：

CABRERA, M. O. R. D. O. N. E. Z. ^{[1
]}

ROSALSKY, A. ^{[2
]}

UNVER, M. ^{[3
]}

VOLODIN, A. ^{[4
,5
,6
]}

机构：

[1] Univ Seville, Dept Math Anal, Seville, Spain

[2] Univ Florida, Dept Stat, Gainesville, FL 32611 USA

[3] Ankara Univ, Dept Math, Fac Sci, Ankara, Turkey

[4] Xiamen Univ Technol, Sino Canada Res Ctr Nonlinear Dynam & Noise Contr, Xiamen, Peoples R China

[5] Xiamen Univ Technol, Univ Regina, Xiamen, Fujian, Peoples R China

[6] Univ Regina, Dept Math & Stat, Regina, SK S4S 0A2, Canada

来源：

THEORY OF PROBABILITY AND ITS APPLICATIONS | 2022年 / 67卷 / 01期

关键词：

uniform integrability; power series summability method; L-1; -convergence; STATISTICAL CONVERGENCE; WEIGHTED SUMS; APPROXIMATION; OPERATORS; THEOREMS; SPACES; LAW;

D O I：

10.1137/S0040585X97T990770

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Uniform integrability is an interesting concept in probability theory and functional analysis since it plays an important role in establishing laws of large numbers. In the literature, there are several versions of uniform integrability. Some are defined with the help of matrix summability methods, such as the Ces??ro matrix, or more general methods. In this paper, we introduce a new version of uniform integrability via power series summability methods. We investigate the relationships of this new concept with some previous concepts and give L1- and L2-convergence results for the laws of large numbers.

引用

页码：89 / 104

页数：16

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