Summability of Double Independent Random Variables. (20th July 2008)

• Record Type: Journal Article
• Authors: Patterson, Richard F.; Savaş, Ekrem
• Other Names: Dshalalow Jewgeni Academic Editor.
• Is Part Of: Journal of inequalities and applications. Volume 2008(2008)
• Publication Date: 2008-07-20
• Subjects: Inequalities (Mathematics) -- Periodicals; 512.97
• DOI: 10.1155/2008/948195
• Languages: English
• ISSNs: 1029-242X

Abstract

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. Ifmax k, l | a m, n, k, l | = max k, l | a m, k a n, l | = O ( m − γ 1 ) O ( n − γ 2 ), γ 1, γ 2 > 0, thenE | X ⌣ | 1 + 1 / γ 1 < ∞ andE | X ⌣ ⌣ | 1 + 1 / γ 2 < ∞ imply thatY m, n → μ almost sure P-convergence.