Geodesic
Limit laws for cumulative sums of independent random variables with distributions of a~finite number of types
Teoriâ veroâtnostej i ee primeneniâ, Tome 16 (1971) no. 4, pp. 614-637

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Let $Z_n=\frac1{B_n}\sum_{j=1}^nX_j-A_n$ ($n=1,2,\dots$) be a sequence of normalized sums of random variables with a non-degenerate limit distribution function $G(x)$. The paper describes classes $\mathfrak G_r$ of possible $G(x)$ when the distributions of $X_j$ ($j=1,2,\dots$) belong to at most $r$ ($r=1,2,\dots$) different types. 
@article{TVP_1971_16_4_a1,
     author = {A. A. Zinger},
     title = {Limit laws for cumulative sums of independent random variables with distributions of a~finite number of types},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {614--637},
     publisher = {mathdoc},
     volume = {16},
     number = {4},
     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1971_16_4_a1/}
}
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A. A. Zinger. Limit laws for cumulative sums of independent random variables with distributions of a~finite number of types. Teoriâ veroâtnostej i ee primeneniâ, Tome 16 (1971) no. 4, pp. 614-637. http://geodesic.mathdoc.fr/item/TVP_1971_16_4_a1/