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The Law of Large Numbers for Product Partial Sum Processes Indexed by Sets

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  • Kwon, J. S.

Abstract

Let N = {1, 2, ...} and let {Xi:i [set membership, variant] Nd1} and {Yj:j [set membership, variant] Nd2} be two families of i.i.d. integrable random variables. Let S(nA) be the sum of those XiYj's for which A [subset of] [0,1]d, d = d1 + d2 and (i/n,,j/n) [set membership, variant] A. It is proved that S(·) satisfies a strong law of large numbers that is uniform over , where is a family of subsets of [0, 1]d satisfying some conditions.

Suggested Citation

  • Kwon, J. S., 1994. "The Law of Large Numbers for Product Partial Sum Processes Indexed by Sets," Journal of Multivariate Analysis, Elsevier, vol. 49(1), pages 76-86, April.
    • Handle: RePEc:eee:jmvana:v:49:y:1994:i:1:p:76-86
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