Abstract
The well-known characterization indicated in the title involves the moving maximal dyadic averages of the sequence (X k : k = 1, 2, …) of random variables in Probability Theory. In the present paper, we offer another characterization of the SLLN which does not require to form any maximum. Instead, it involves only a specially selected sequence of moving averages. The results are also extended for random fields (X kℓ: k, ℓ = 1, 2, …).
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Dedicated to Professors Endre Csáki and Pál Révész on the occasion of their 75th birthdays
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Móricz, F. Necessary and sufficient conditions for the strong law of large numbers. Period Math Hung 62, 61–73 (2011). https://doi.org/10.1007/s10998-011-5061-8
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DOI: https://doi.org/10.1007/s10998-011-5061-8