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International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 3, Pages 587-591
doi:10.1155/S0161171293000729

On strong laws of large numbers for arrays of rowwise independent random elements

Abolghassem Bozorgnia,1 Ronald Frank Patterson,2 and Robert Lee Taylor3

1Department of Statistics, Mashhad University, Mashhad, Iran
2Department of Mathematics and Computer Science, Georgia State University, Atlanta 30303, Ga, USA
3Department of Statistics, University of Georgia, Athens 30602, Ga, USA

Received 19 March 1992; Revised 7 April 1992

Copyright © 1993 Hindawi Publishing Corporation. 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

Let {Xnk} be an array of rowwise independent random elements in a separable Banach space of type r, 1≤r≤2. Complete convergence of n1/p∑k=1nXnk to 0, 0<p<r≤2 is obtained when sup1≤k≤nE ‖Xnk‖v=O(nα), α≥0 with v(1p−1r)>α+1. An application to density estimation is also given.