文档介绍：Downloaded By: [Universidad de Sevilla] At: 09:43 19 March 2007 Stochastic Analysis and Applications , 25: 281–291, 2007 Copyright ? Taylor & Francis Group, LLC ISSN 0736-2994 print/1532-9356 online DOI: plete Convergence for Arrays of Random Elements and Variables Víctor Hernández Departamento de Estadística e Investigación Operativa, de la Universidad Nacional de Educación a Distancia, Madrid, Spain Henar a Departamento de Estadística e Investigación Operativa, de la Universidad Pública de Navarra, Pamplona, Spain Andrei Volodin Department of Mathematics and Statistics, University of Regina, Regina, Saskatchewan, Canada Abstract: We plete convergence results for arrays of row-wise independent Banach space valued random elements. The main result deals with two cases that usually are considered separately: when no assumptions are made concerning the geometry of the underlying Banach space and when the Banach space is of Rademacher type p . Keywords: Array of Banach space valued random elements; Complete conver- gence; Convergence in probability; Domination conditions; Normed partial sums; Row-wise independence; Type pBanach space. AMS Classi?cation: 60B12; 60F05; 60F25; 60G42. Accepted November 2, 2006 The authors are grateful to the referee for offering some valuable suggestions which enabled them to improve the overall presentation. The work of A. Volodin is supported by a grant from the Natural Sciences and Engineering Research Council of Canada. Address correspondence to Henar a, Departamento de Estadística e Investigación Operativa, de la Universidad Pública de Navarra, Pamplona, Spain; E-mail: ******@ Downloaded By: [Universidad de Sevilla] At: 09:43 19 March 2007 282 Hernández et al. I. INTRODUCTION AND PRELIMINARIES The concept plete convergence was introduced in [1] as follows. A sequence of random variables ?U n ?n ≥ 1 ? is said to pletely to a constant c if ?? n = 1 P?? U n ? c ?>??< ? for all ?>