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
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.