Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 569759, 14 pages
doi:10.1155/2010/569759
Research Article

A Hájek-Rényi-Type Maximal Inequality and Strong Laws of Large Numbers for Multidimensional Arrays

Nguyen Van Quang1 and Nguyen Van Huan2

1Department of Mathematics, Vinh University, Nghe An 42000, Vietnam
2Department of Mathematics, Dong Thap University, Dong Thap 871000, Vietnam

Received 1 July 2010; Accepted 27 October 2010

Academic Editor: Alexander I. Domoshnitsky

Copyright © 2010 Nguyen Van Quang and Nguyen Van Huan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A Hájek-Rényi-type maximal inequality is established for multidimensional arrays of random elements. Using this result, we establish some strong laws of large numbers for multidimensional arrays. We also provide some characterizations of Banach spaces.