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International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 1, Pages 135-144
doi:10.1155/S0161171285000126

Strong laws of large numbers for arrays of row-wise exchangeable random elements

Robert Lee Taylor1 and Ronald Frank Patterson2

1Department of Statistics and Computer Science, University of Georgia, Athens 30602, GA, USA
2Department of Mathematics, Georgia State University, Atlanta 30303, GA, USA

Received 1 October 1984

Copyright © 1985 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,1≤k≤n,n≤1} be a triangular array of row-wise exchangeable random elements in a separable Banach space. The almost sure convergence of n−1/p∑k=1nXnk,1≤p<2, is obtained under varying moment and distribution conditions on the random elements. In particular, strong laws of large numbers follow for triangular arrays of random elements in(Rademacher) type p separable Banach spaces. Consistency of the kernel density estimates can be obtained in this setting.