International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 8, Pages 1317-1320
doi: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 Le Van Thanh. 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∈ℤ+d} such that {|Xn|p,n∈ℤ+d} is uniformly integrable
for some 0<p<2, the Lp-convergence is established for the sums (1/|n|1/p) (∑j≺n(Xj−aj)), where aj=0 if 0<p<1, and aj=EXj if 1≤p<2.