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Necessary conditions in the law of large numbers for martingales and associated systems. (English. Russian original) Zbl 1234.60030

Russ. Math. Surv. 66, No. 4, 822-824 (2011); translation from Usp. Mat. Nauk 66, No. 4, 181-182 (2011).
From the paper: Typically, necessary and sufficient conditions in classical limit theorems for independent random variables have their natural counterparts for martingales. However, in the martingale case, these counterparts usually provide only sufficient conditions. In this note, we investigate minimal restrictions under which the conditions of the standard law of large numbers for martingale series are necessary conditions.

MSC:

60F05 Central limit and other weak theorems
60G42 Martingales with discrete parameter
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