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On the Skitovich-Darmois Theorem on Abelian Groups

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.

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 10, pp. 1342 – 1356, October, 2004.

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Myronyuk, M.V. On the Skitovich-Darmois Theorem on Abelian Groups. Ukr Math J 56, 1602–1618 (2004). https://doi.org/10.1007/s11253-005-0137-3

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  • DOI: https://doi.org/10.1007/s11253-005-0137-3

Keywords

  • Abelian Group
  • Linear Form
  • Independent Random Variable
  • Compact Abelian Group