Abstract
LetJ={1,2,...}d and let {X j, j∈J} be an α-mixing sequence which is not necessarily stationary and letS(nA) be the sum of allX j for whichj/n∈A. It is proved in this paper thatS(·) satisfies the strong law of large numbers that is uniform overA∈A, whereA is a family of subsets of [0, 1]d satisfying a mild condition.
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Bing, X. Strong laws for α=mixing sequence processes indexed by sets. Appl. Math. 10, 45–48 (1995). https://doi.org/10.1007/BF02663893
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DOI: https://doi.org/10.1007/BF02663893