Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 68605, 6 pages
Mean convergence theorem for multidimensional arrays of random elements in Banach spaces
Department of Mathematics, Vinh University, Nghe An 42118, Vietnam
Received 2 March 2006; Revised 29 June 2006; Accepted 12 July 2006
Copyright © 2006 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.
For a -dimensional array of random elements in a real separable stable type () Banach space, a mean convergence theorem is established. Moreover, the conditions
for the convergence in mean of order are shown to completely characterize stable-type Banach spaces.