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A Hájek-Rényi-type maximal inequality and strong laws of large numbers for multidimensional arrays. (English) Zbl 1215.60022

Summary: A Hájek-Rényi-type maximal inequality is established for multidimensional arrays of random elements. Using this result, we establish some strong laws of large numbers for multidimensional arrays. We also provide some characterizations of Banach spaces.

MSC:

60F15 Strong limit theorems
60E15 Inequalities; stochastic orderings
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