A note on complete convergence for arrays

Abstract

We extend and generalize some recent results on complete convergence for independent non-identically distributed random variables (cf. Duncan and Szynal, 1984; Gut, 1992; Hu et al., 1989). In the main result no assumptions are made concerning the existence of expected values or absolute moments of the random variables. Some well-known results from the literature can be easily obtained from our theorem. © 1998 Elsevier Science B.V. All rights reserved.