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Mat. Zametki, 1977, Volume 22, Issue 5, Pages 759–762 (Mi mz8097)  

This article is cited in 1 scientific paper (total in 1 paper)

A characterization of Gaussian measures on locally compact Abelian groups

B. L. S. Prakasa Rao

Indian Statistics Institute

Abstract: Let $\xi$ and $\eta$ be independent random variables having equal variance. In order that $\xi+\eta$ and $\xi-\eta$ be independent, it is necessary and sufficient that $\xi$ and $\eta$ have normal distributions. This result of Bernshtein [1] is carried over in [7] to the case when $\xi$ and $\eta$ take values in a locally compact Abelian group. In the present note, a characterization of Gaussian measures on locally compact Abelian groups is given in which in place of $\xi+\eta$ and $\xi-\eta$, functions of $\xi$ and $\eta$ are considered which satisfy the associativity equation.

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English version:
Mathematical Notes, 1977, 22:5, 914–916

Bibliographic databases:

UDC: 519.2
Received: 06.06.1977

Citation: B. L. S. Prakasa Rao, “A characterization of Gaussian measures on locally compact Abelian groups”, Mat. Zametki, 22:5 (1977), 759–762; Math. Notes, 22:5 (1977), 914–916

Citation in format AMSBIB
\Bibitem{Pra77}
\by B.~L.~S.~Prakasa~Rao
\paper A characterization of Gaussian measures on locally compact Abelian groups
\jour Mat. Zametki
\yr 1977
\vol 22
\issue 5
\pages 759--762
\mathnet{http://mi.mathnet.ru/mz8097}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=464349}
\zmath{https://zbmath.org/?q=an:0371.60011}
\transl
\jour Math. Notes
\yr 1977
\vol 22
\issue 5
\pages 914--916
\crossref{https://doi.org/10.1007/BF01098357}


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    This publication is cited in the following articles:
    1. M. V. Mironyuk, G. M. Feldman, “Independent linear statistics on the two-dimensional torus”, Theory Probab. Appl., 52:1 (2008), 78–92  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Математические заметки Mathematical Notes
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