Geodesic
On the membership of lattice probability distributions in the class~$I_0$
Izvestiya. Mathematics , Tome 11 (1977) no. 2, pp. 441-452.

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Necessary and sufficient conditions are obtained for an infinitely divisible lattice law to belong to the class $I_0$, when its Lévy–Hinčin spectral measure $G(x)$ satisfies the condition $$ \int\limits_{|x|>y}dG(x)=O(e^{-\rho y\ln y}),\qquad\exists\rho>0,\quad y\to\infty. $$ Bibliography: 10 titles. 
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A. E. Fryntov; G. P. Chistyakov. On the membership of lattice probability distributions in the class~$I_0$. Izvestiya. Mathematics , Tome 11 (1977) no. 2, pp. 441-452. http://geodesic.mathdoc.fr/item/IM2_1977_11_2_a12/

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