Necessary and sufficient conditions for the strong law of large numbers (Q653798)
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scientific article; zbMATH DE number 5990582
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Necessary and sufficient conditions for the strong law of large numbers |
scientific article; zbMATH DE number 5990582 |
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Necessary and sufficient conditions for the strong law of large numbers (English)
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19 December 2011
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The author proves a characterization of the strong law of large numbers for i.i.d.\ random variables using a specially selected sequence of moving averages; his conditions are optimal, and several examples complete the paper. The new results simplify the classical characterization with maximal moving dyadic averages.
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sequences of random variables
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SLLN
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moving averages
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Toeplitz's theorem
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random fields
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moving rectangular averages
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bounded convergence in Pringsheim's sense
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Robison's theorem in summability theory
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