Geodesic
On the Skitovich--Darmois Theorem for $\mathbf{a}$-Adic Solenoids
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 9 (2013), pp. 582-593.

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By the Skitovich–Darmois theorem, the Gaussian distribution on the real line is characterized by the independence of two linear forms of $n$ independent random variables. The theorem is known to fail for a compact connected Abelian group even in the case when $n=2$. In the paper, it is proved that a weak analogue of the Skitovich–Darmois theorem holds for some $\mathbf{a}$-adic solenoids if we consider three independent linear forms of three random variables. 
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I. P. Mazur. On the Skitovich--Darmois Theorem for $\mathbf{a}$-Adic Solenoids. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 9 (2013), pp. 582-593. http://geodesic.mathdoc.fr/item/JMAG_2013_9_a6/

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