Geodesic
On the law of the iterated logarithm for a sequence of independent random variables with finite variances
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 4, Tome 278 (2001), pp. 182-186

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Sufficient conditions are fiven for the applicability of the law of the iterated logarithm to a sequence of independent random variables having finite variances. 
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     author = {V. V. Petrov},
     title = {On the law of the iterated logarithm for a sequence of independent random variables with finite variances},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {182--186},
     publisher = {mathdoc},
     volume = {278},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2001_278_a9/}
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V. V. Petrov. On the law of the iterated logarithm for a sequence of independent random variables with finite variances. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 4, Tome 278 (2001), pp. 182-186. http://geodesic.mathdoc.fr/item/ZNSL_2001_278_a9/