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

Recommended by Jewgeni Dshalalow

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.