Geodesic
On the law of large numbers for martingales
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Stochastic calculus, martingales, and their applications, Tome 287 (2014), pp. 300-309

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Additional constraints are obtained under which sufficient conditions in the classical law of large numbers in a scheme of series for martingales are also necessary. The accuracy of the constraints obtained is demonstrated by examples. 
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     author = {P. A. Yaskov},
     title = {On the law of large numbers for martingales},
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     year = {2014},
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     url = {http://geodesic.mathdoc.fr/item/TM_2014_287_a16/}
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P. A. Yaskov. On the law of large numbers for martingales. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Stochastic calculus, martingales, and their applications, Tome 287 (2014), pp. 300-309. http://geodesic.mathdoc.fr/item/TM_2014_287_a16/