Journal of Applied Mathematics and Stochastic Analysis 
Volume 2006 (2006), Article ID 68605, 6 pages
doi:10.1155/JAMSA/2006/68605

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

Abstract

For a d-dimensional array of random elements {Vn,n∈ℤ+d} in a real separable stable type p (1≤p<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.