Geodesic
More on the Skitovich--Darmous theorem for finite Abelian groups
Teoriâ veroâtnostej i ee primeneniâ, Tome 45 (2000) no. 3, pp. 603-607

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The following theorem is proved. Let $X$ be a finite Abelian group and $\xi_1, \xi_2$ be independent random variables with values in $X$ and with distributions $\mu_1, \mu_2$. Then the independence of the linear statistics $L_1=\alpha_1(\xi_1) + \alpha_2(\xi_2)$ and $L_2=\beta_1(\xi_1) + \beta_2(\xi_2)$, where $\alpha_j, \beta_j$ are automorphisms of the group $X$, implies that $\mu_1,\mu_2$ are idempotent distributions.
Keywords: characterization of probability distributions, independence of linear statistics, finite Abelian group. 
@article{TVP_2000_45_3_a12,
     author = {G. M. Feldman},
     title = {More on the {Skitovich--Darmous} theorem for finite {Abelian} groups},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {603--607},
     publisher = {mathdoc},
     volume = {45},
     number = {3},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2000_45_3_a12/}
}
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G. M. Feldman. More on the Skitovich--Darmous theorem for finite Abelian groups. Teoriâ veroâtnostej i ee primeneniâ, Tome 45 (2000) no. 3, pp. 603-607. http://geodesic.mathdoc.fr/item/TVP_2000_45_3_a12/