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Characterizations of invariant distributions

Published online by Cambridge University Press:  24 October 2008

Timothy C. Brown ,
Donald I. Cartwright  and
G. K. Eagleson
Timothy C. Brown
Affiliation:
Department of Statistics, University of Melbourne, Parkville, Vic., 3052
Donald I. Cartwright
Affiliation:
Department of Pure Mathematics, University of Sydney, N.S.W., 2006
G. K. Eagleson
Affiliation:
C.S.I.R.O., Division of Mathematics and Statistics, P.O. Box 218, Lindfield, N.S.W., 2070
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Abstract

Let (S, ρ) be a separable metric space and G a group of transformations of S. Necessary and sufficient conditions for a distribution on S to be invariant under G are derived in terms of the behaviour of the convolution of a random transformation from G and a random element of S.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 97 , Issue 2 , March 1985 , pp. 349 - 355
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

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