Abstract

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.