2017
Том 69
№ 6

All Issues

On the Skitovich-Darmois Theorem on Abelian Groups

Myronyuk M. V.

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Abstract

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.

English version (Springer): Ukrainian Mathematical Journal 56 (2004), no. 10, pp 1602-1618.

Citation Example: Myronyuk M. V. On the Skitovich-Darmois Theorem on Abelian Groups // Ukr. Mat. Zh. - 2004. - 56, № 10. - pp. 1342 – 1356.

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