The Hajek-Renyi-Chow maximal inequality and a strong law of large numbers in Riesz spaces

被引：2
|
作者：
Kuo, Wen-Chi [1 ]
Rodda, David F. [1 ]
Watson, Bruce A. [1 ]
机构：
[1] Univ Witwatersrand, Sch Math, Private Bag 3, ZA-2050 Johannesburg, South Africa
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2020年 / 481卷 / 01期
基金：
新加坡国家研究基金会;
关键词：
Riesz spaces; Vector lattices; Maximal inequality; Clarkson's inequality; Submartingale convergence; Strong law of large numbers; CONVERGENCE;
D O I：
10.1016/j.jmaa.2019.123462
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we generalize the Hajek-Renyi-Chow maximal inequality for submartingales to L-P type Riesz spaces with conditional expectation operators. As applications we obtain a submartingale convergence theorem and a strong law of large numbers in Riesz spaces. Along the way we develop a Riesz space variant of the Clarkson's inequality for 1 <= p <= 2. (C) 2019 Elsevier Inc. All rights reserved.
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页数：10
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