Geodesic
On a Hypothesis Proposed by B.\,V.~Gnedenko
Teoriâ veroâtnostej i ee primeneniâ, Tome 6 (1961) no. 4, pp. 469-474

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Several years ago Academician B. V. Gnedenko proposed the following: Let $\xi_n=(1/B_n)(\xi_1+\cdots+\xi_n)-A_n$ be a sequence of normed sums of independent stochastic quantities having a nondegenerate limit distribution $G(x)$ for appropriately selected constants $A_n$ and $B_n$. If among the distributions of stochastic quantities $\xi _i $ there are only $s$ different ones, then the limit distribution $G(x)$ is a composition of not more than stable laws. In the paper the hypothesis proposed by B. V. Gnedenko is proved for $s=2$ and an example is presented showing that the theorem by E. Lebedintseva [2] does not prove this hypothesis in its entirety. 
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     author = {V. M. Zolotarev and V. S. Korolyuk},
     title = {On a {Hypothesis} {Proposed} by {B.\,V.~Gnedenko}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {469--474},
     publisher = {mathdoc},
     volume = {6},
     number = {4},
     year = {1961},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1961_6_4_a10/}
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V. M. Zolotarev; V. S. Korolyuk. On a Hypothesis Proposed by B.\,V.~Gnedenko. Teoriâ veroâtnostej i ee primeneniâ, Tome 6 (1961) no. 4, pp. 469-474. http://geodesic.mathdoc.fr/item/TVP_1961_6_4_a10/