Geodesic
A generalization of the Kolmogorov theorem on the law of the iterated logarithm
Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 1, pp. 134-143 Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper gives necessary and sufficient conditions for the fulfillment of the law of the iterated logarithm for a sum of bounded random variables in the case of arbitrary norming monotonically tending to infinity. For the standard norming sequence the results obtained imply the known Kolmogorov theorem.
Keywords: bounded independent random variables, law of the iterated logarithm, convergence almost surely. 
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     author = {L. V. Rozovskii},
     title = {A generalization of the {Kolmogorov} theorem on the law of the iterated logarithm},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {134--143},
     year = {1997},
     volume = {42},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1997_42_1_a8/}
}
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L. V. Rozovskii. A generalization of the Kolmogorov theorem on the law of the iterated logarithm. Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 1, pp. 134-143. http://geodesic.mathdoc.fr/item/TVP_1997_42_1_a8/