Geodesic
On conditions for convergence of sums of independent variables
Teoriâ veroâtnostej i ee primeneniâ, Tome 40 (1995) no. 4, pp. 919-924

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The paper is devoted to nonclassical conditions for the weak convergence of distributions of sums of independent random variables to fixed distributions. The proposed conditions for sums convergence are formulated in terms of “closeness” of summands distributions to elements of expansion of a limit distribution in some integral metrics.
Keywords: nonclassical conditions for convergence, integral metrics. 
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     author = {A. G. Sholomitskii},
     title = {On conditions for convergence of sums of independent variables},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {919--924},
     publisher = {mathdoc},
     volume = {40},
     number = {4},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1995_40_4_a20/}
}
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A. G. Sholomitskii. On conditions for convergence of sums of independent variables. Teoriâ veroâtnostej i ee primeneniâ, Tome 40 (1995) no. 4, pp. 919-924. http://geodesic.mathdoc.fr/item/TVP_1995_40_4_a20/