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International Journal of Mathematics and Mathematical Sciences
Volume 8, Issue 4, Pages 805-812

A note on convergence of weighted sums of random variables

1Department of Mathematics, Jilin University, Changchun, China
2Department of Probability & Statistics, The University, Sheffield S3 7RH, UK
3University of Pittsburgh, Pittsburgh, Pennsylvania, USA

Received 3 January 1984; Revised 25 July 1984

Copyright © 1985 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.


Under uniform integrability condition, some Weak Laws of large numbers are established for weighted sums of random variables generalizing results of Rohatgi, Pruitt and Khintchine. Some Strong Laws of Large Numbers are proved for weighted sums of pairwise independent random variables generalizing results of Jamison, Orey and Pruitt and Etemadi.