STRONG LAWS FOR α-MIXING SEQUENCE PROCESSES INDEXED BY SETS
Xubing · Acta Scientiarum Naturalium Universitatis Sunyatseni · 1995
Let J = {1,2,... }^d and let {Xj,j ∈ J} be an α-mixing sequence which is not necessarily stationary and let S(nA) be the sum of all Xj for which j/n ∈ A. It is proved in this paper that S(·) satisfies the strong law of large numbers that is uniform over A ∈ A, where A is a family of subsets of [0, l]^d satisfying a mild condition.