Geodesic
On the law of the iterated logarithm for sequences of dependent random variables
Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part VI, Tome 97 (1980), pp. 186-194

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Some sufficient conditions are found for the applicability of the law.of the iterated logarithm to sequences of $m$-dependent random variables with finite variances. 
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     author = {V. V. Petrov},
     title = {On the law of the iterated logarithm for sequences of dependent random variables},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {186--194},
     publisher = {mathdoc},
     volume = {97},
     year = {1980},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1980_97_a17/}
}
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V. V. Petrov. On the law of the iterated logarithm for sequences of dependent random variables. Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part VI, Tome 97 (1980), pp. 186-194. http://geodesic.mathdoc.fr/item/ZNSL_1980_97_a17/