On the Skitovich-Darmois Theorem on Abelian Groups - Myronyuk, M. V. (Ukrains’kyi Matematychnyi Zhurnal, 2004)
We prove theorems that generalize the Skitovich-Darmois theorem to the case where independent random variables ξj, j = 1, 2, ..., n, n ≥ 2, take values in a locally compact Abelian group and the coefficients αj and βj of the linear forms L 1 = α1ξ1 + ... + αnξn and L 2 = β1ξ1 + ... + βnξn are automorphisms of this group.