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International Journal of Mathematics and Mathematical Sciences
Volume 20, Issue 4, Pages 773-782

On complete convergence for randomly indexed sums for a case without identical distributions

1Technical University of Lublin, Department of Applied Mathematics, Bernardyńska 13, Lublin 20-950 , Poland
2Institute of Mathematics, UMCS Plac Marii Curie-Skłodowskiej 1, Lublin 20-031, Poland

Received 26 December 1995; Revised 10 August 1996

Copyright © 1997 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.


In this note we extend the complete convergence for randomly indexed sums given by Klesov (1989) to nonidentical distributed random variables.