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Independent linear forms on connected Abelian groups
Author(s) -
Feldman Gennadiy,
Myronyuk Margaryta
Publication year - 2011
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200810101
Subject(s) - mathematics , abelian group , gaussian , random variable , independence (probability theory) , gaussian random field , multivariate random variable , pure mathematics , gaussian function , statistics , physics , quantum mechanics
According to the classical Skitovich‐Darmois theorem the independence of two linear forms of independent random variables implies that the random variables are Gaussian. We prove an analog of this theorem for some locally compact Abelian groups. It turns out that in the considered case the random variables are either Gaussian or their distributions are convolutions of Gaussian distributions and some signed measures. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim