Email this article Mean Convergence Theorems and Weak Laws of Large Numbers for Arrays of Measurable Operators under Some Conditions of Uniform Integrability
- Authors: Quang N.V.1, Son D.T.2, Hu T.1, Huan N.V.3,4
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Affiliations:
- Department of Mathematics
- Faculty of Fundamental Science
- Institute for Computational Science and Technology (ICST)
- Department of Mathematics and Applications
- Issue: Vol 40, No 8 (2019)
- Pages: 1218-1229
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/205421
- DOI: https://doi.org/10.1134/S1995080219080249
- ID: 205421
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Abstract
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.
About the authors
Nguyen Van Quang
Department of Mathematics
Author for correspondence.
Email: nvquang@hotmail.com
Viet Nam, Vinh, Nghe An Province
Do The Son
Faculty of Fundamental Science
Author for correspondence.
Email: dotheson@iuh.edu.vn
Viet Nam, Ho Chi Minh City
Tien-Chung Hu
Department of Mathematics
Author for correspondence.
Email: tchu@math.nthu.edu.tw
Taiwan, Province of China, Hsinchu, Taiwan
Nguyen Van Huan
Institute for Computational Science and Technology (ICST); Department of Mathematics and Applications
Author for correspondence.
Email: vanhuandhdt@yahoo.com
Viet Nam, Ho Chi Minh City; Ho Chi Minh City
