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International Journal of Mathematics and Mathematical Sciences
Volume 17, Issue 1, Pages 1-14

On complete convergence in a Banach space

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

Copyright © 1994 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.