Geodesic
On a~class of limit distributions for normed sums of independent random variables
Teoriâ veroâtnostej i ee primeneniâ, Tome 10 (1965) no. 4, pp. 672-692

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Let $\zeta_n=\frac{\xi_1+\xi_2+\dots+\xi_n}{B_n}-A_n$ ($n=1,2,\dots$) be a sequence of normed sums $n$ of independent random variables which has a nondegenerate limit distribution $G(x)$ for appropriately selected constants $A_n$, $B_n$. This paper is devoted to the characterization of the class $\{G(x)\}$ named here $\mathscr P_r$ arizing when among the distributions of the random variables $\xi^i$ there are only $r$ different ones. Three theorems describing the class $\mathscr P_r$ are proved 
@article{TVP_1965_10_4_a4,
     author = {A. A. Zinger},
     title = {On a~class of limit distributions for normed sums of independent random variables},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {672--692},
     publisher = {mathdoc},
     volume = {10},
     number = {4},
     year = {1965},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1965_10_4_a4/}
}
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A. A. Zinger. On a~class of limit distributions for normed sums of independent random variables. Teoriâ veroâtnostej i ee primeneniâ, Tome 10 (1965) no. 4, pp. 672-692. http://geodesic.mathdoc.fr/item/TVP_1965_10_4_a4/