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  • THE SKITOVICH–DARMOIS THEOREM FOR LOCALLY COMPACT ABELIAN GROUPS

  • Part of
  • GENNADIY FELDMAN, PIOTR GRACZYK
  • Journal:
    Journal of the Australian Mathematical Society / Volume 88 / Issue 3 / June 2010
    Published online by Cambridge University Press:
    11 June 2010, pp. 339-352
    Print publication:
    June 2010
    • Article
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  • According to the Skitovich–Darmois theorem, the independence of two linear forms of n independent random variables implies that the random variables are Gaussian. We consider the case where independent random variables take values in a second countable locally compact abelian group X, and coefficients of the forms are topological automorphisms of X. We describe a wide class of groups X for which a group-theoretic analogue of the Skitovich–Darmois theorem holds true when n=2.