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Zh. Mat. Fiz. Anal. Geom., 2014, Volume 10, Number 1, Pages 126–133 (Mi jmag585)  

On a Characterization of the Haar Distribution on Compact Abelian Groups

I. P. Mazur

B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, 47 Lenin Ave., Kharkiv 61103, Ukraine

Abstract: We prove a theorem which characterizes the Haar distribution on a compact Abelian group by the independence of n linear forms of n independent random variables. The coefficients of the forms are continuous endomorphisms of the group.

Key words and phrases: compact Abelian group, linear form.

DOI: https://doi.org/10.15407/mag10.01.126

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MSC: 39B99, 43A25, 60B15, 62E10
Received: 12.11.2013
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Citation: I. P. Mazur, “On a Characterization of the Haar Distribution on Compact Abelian Groups”, Zh. Mat. Fiz. Anal. Geom., 10:1 (2014), 126–133

Citation in format AMSBIB
\Bibitem{Maz14}
\by I.~P.~Mazur
\paper On a Characterization of the Haar Distribution on Compact Abelian Groups
\jour Zh. Mat. Fiz. Anal. Geom.
\yr 2014
\vol 10
\issue 1
\pages 126--133
\mathnet{http://mi.mathnet.ru/jmag585}
\crossref{https://doi.org/10.15407/mag10.01.126}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3236963}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000333090600004}


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