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

Le Van Thanh

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 d-dimensional array of random elements {Vn,n+d} in a real separable stable type p (1p<2) Banach space, a mean convergence theorem is established. Moreover, the conditions for the convergence in mean of order p are shown to completely characterize stable-type p Banach spaces.