International Journal of Mathematics and Mathematical Sciences 
Volume 17 (1994), Issue 1, Pages 1-14
doi:10.1155/S0161171294000013

On complete convergence in a Banach space

Anna Kuczmaszewska1 and Dominik Szynal2

 1Technical University, ul. Bernardyńska 13, Lublin 20-109, Poland
2Institute of Mathematics, UMCS, Piac Marii Curie-Sklodowskiej 1, Lublin 20-031, Poland
Received 19 May 1992; Revised 1 January 1993

Abstract

Sufficient conditions are given under which a sequence of independent random elements taking values in a Banach space satisfy the Hsu and Robbins law of large numbers. The complete convergence of random indexed sums of random elements is also considered.