International Journal of Mathematics and Mathematical Sciences
Volume 10 (1987), Issue 4, Pages 805-814
Strong laws of large numbers for arrays of rowwise independent random elements
1Depatment of statistics , University of Georgia, Athens 30602, GA, USA
2Depatment of Mathematics, National Tsing-Hua University, Hsin-chu, Taiwan
Received 18 November 1986
Copyright © 1987 Robert Lee Taylor and Tien-Chung Hu. 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.
Let be an array of rowwise independent random elements in a separable
Banach space of type with for all , . The complete convergence (and hence almost sure convergence) of , , is obtained when are uniformly bounded by a random variable with . When the array consists of i.i.d, random elements, then it is shown that converges completely to if and only if .