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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:481

Article

Kuo, Wen-Chi¹  Rodda, David F.¹  Watson, Bruce A.¹ 

[1] Univ Witwatersrand, Sch Math, Private Bag 3, ZA-2050 Johannesburg, South Africa

关键词: Riesz spaces;    Vector lattices;    Maximal inequality;    Clarkson's inequality;    Submartingale convergence;    Strong law of large numbers;   

DOI  :  10.1016/j.jmaa.2019.123462

来源: Elsevier

【 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.

【 授权许可】

Free