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. In this paper we introduce the concept of asymptot-ically almost negatively associated random variables in a Hilbertspace and obtain the strong law of large numbers for a strictlystationary asymptotically almost negatively associated sequence ofH-valued random variables with zero means and nite second mo-ments. As an application we prove a strong law of large numbersfor a linear process generated by asymptotically almost negativelyrandom variables in a Hilbert space with this result. 1. Introduction A nite family fY i ; 1 • i • ng of real-valued random variables issaid to be associated if for any coordinatewise increasing functions f;g :R n ! R Cov ( f ( Y 1 ;¢¢¢ ;Y n ) ;g ( Y 1 ;¢¢¢ ;Y n )) ‚ 0whenever this covariance exists. A nite family fY i ; 1 • i • ng issaid to be negatively associated(NA) if for any disjoint subsets A;B ‰f 1 ;¢¢¢ ;ng and any real coordinatewise nondecreasing functions f onR A , g on R B , Cov ( f ( Y i ;i 2 A ) ;g ( Y j ;j 2 B )) • 0whenever the covariance exists. An innite family of random vari-ables is associated(negatively associated) if every nite subfamily isassociated(negatively associated). These concepts of dependence were

A STRONG LAW OF LARGE NUMBERS FOR AANA RANDOM VARIABLES IN A HILBERT SPACE AND ITS APPLICATION