Geodesic
A generalization of theorems due to H. Cramer and Yu. V. Linnik–V. P. Skitovič
Teoriâ veroâtnostej i ee primeneniâ, Tome 15 (1970) no. 2, pp. 345-350 
G. P. Chistyakov. A generalization of theorems due to H. Cramer and Yu. V. Linnik–V. P. Skitovič. Teoriâ veroâtnostej i ee primeneniâ, Tome 15 (1970) no. 2, pp. 345-350. http://geodesic.mathdoc.fr/item/TVP_1970_15_2_a15/
@article{TVP_1970_15_2_a15,
     author = {G. P. Chistyakov},
     title = {A~generalization of theorems due to {H.~Cramer} and {Yu.} {V.~Linnik{\textendash}V.} {P.~Skitovi\v{c}}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {345--350},
     year = {1970},
     volume = {15},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1970_15_2_a15/}
}
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Let $B$ be a class of functions $V(x)$ with bounded variation on $(-\infty,\infty)$ satisfying the conditions: 1) $\int_{-\infty}^\infty dV(x)=1$; 2) $V(x)=\omega_1(x)-\omega_2(x)$; where $\omega_j(x)$ are nondecreasing functions $\omega_j(x)+\omega_j(-x)=2\omega_j(0)$, $j=1,2$, and for some $\gamma>0$ $$ \operatorname{Var}\omega_2(x)|_y^\infty=O(e^{-y^{1+\gamma}}),\quad y\to\infty; $$ 3) $\int_{-\infty}^\infty e^{yx}dV(x)\ne0,\quad-\infty. In the paper the following result is obtained Theorem. If $V_1(x)$ and $V_2(x)\in B$ and $V_1*V_2=\Phi$, where $\Phi$ is a normal distribution function, then $V_1$ and $V_2$ are normal (may be degenerate).