Geodesic
On absolute convergence of series of random variables almost surely
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 21, Tome 431 (2014), pp. 140-144

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The paper deals with the conditions of absolute convergence of series of random variables almost surely. The results contain no independence assumptions. A generalization is obtained in analytical terms. 
@article{ZNSL_2014_431_a8,
     author = {V. V. Petrov},
     title = {On absolute convergence of series of random variables almost surely},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {140--144},
     publisher = {mathdoc},
     volume = {431},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2014_431_a8/}
}
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V. V. Petrov. On absolute convergence of series of random variables almost surely. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 21, Tome 431 (2014), pp. 140-144. http://geodesic.mathdoc.fr/item/ZNSL_2014_431_a8/