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International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 19, Pages 3195-3198

A note on the strong law of large numbers for associated sequences

Faculty of Mathematics, Shahrood University of Technology, P.O. Box 36155-316, Shahrood, Iran

Received 21 March 2005; Revised 27 April 2005

Copyright © 2005 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.


We prove that the sequence {bn1i=1n(XiEXi)}n1 converges a.e. to zero if {Xn,n1} is anassociated sequence of random variables with n=1bkn2Var(i=kn1+1knXi)< where {bn,n1} is a positive nondecreasing sequence and {kn,n1} is a strictly increasing sequence, both tending to infinity as n tends to infinity and 0<a=infn1bknbkn+11supn1bknbkn+11=c<1.