Journal of Inequalities and Applications
Volume 2008 (2008), Article ID 948195, 12 pages
doi:10.1155/2008/948195
Research Article

Summability of Double Independent Random Variables

Richard F. Patterson1 and Ekrem Savaş2

1Department of Mathematics and Statistics, University of North Florida, 1 UNF Drive, Jacksonville, FL 32224, USA
2Department of Mathematics, Istanbul commerce University, Uskudar, 34672 Istanbul, Turkey

Received 21 May 2008; Accepted 1 July 2008

Academic Editor: Jewgeni Dshalalow

Copyright © 2008 Richard F. Patterson and Ekrem Savaş. 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

We will examine double sequence to double sequence transformation of independent identically distribution random variables with respect to four-dimensional summability matrix methods. The main goal of this paper is the presentation of the following theorem. If max⁡k,l|am,n,k,l|=max⁡k,l|am,kan,l|=O(m−γ1)O(n−γ2), γ1,γ2>0, then E|X⌣|1+1/γ1<∞ and E|X⌣⌣|1+1/γ2<∞ imply that Ym,n→μ almost sure P-convergence.