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International Journal of Mathematics and Mathematical Sciences
Volume 2005, Issue 8, Pages 1317-1320
http://dx.doi.org/10.1155/IJMMS.2005.1317

On the LP-convergence for multidimensional arrays of random variables

Department of Mathematics, Vinh University, Nghe An 42118, Vietnam

Received 14 August 2004; Revised 4 March 2005

Copyright © 2005 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

For a d-dimensional array of random variables {Xn,n+d} such that {|Xn|p,n+d} is uniformly integrable for some 0<p<2, the Lp-convergence is established for the sums (1/|n|1/p)(jn(Xjaj)), where aj=0 if 0<p<1, and aj=EXj if 1p<2.