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A measure invariant under group endomorphisms

Part of: Set functions and measures on spaces with additional structure

Published online by Cambridge University Press:  26 February 2010

J.-M. Belley  and
V. S. Prasad
J.-M. Belley
Affiliation:
Université de Sherbrooke, Sherbrooke, Québec, Canada J1K 2R1.
V. S. Prasad
Affiliation:
Université de Sherbrooke, Sherbrooke, Québec, Canada J1K 2R1.
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Abstract

Let G be a locally compact abelian group. Then there is a finitely additive regular set function m defined on an algebra A of Borel sets in G, m(G) = 1, such that m(T-1F) = m(F) for all F ∈ A and all surjective group endomorphisms T of G onto G.

MSC classification

Secondary: 28C10: Set functions and measures on topological groups or semigroups, Haar measures, invariant measures
Type
Research Article
Information
Mathematika , Volume 29 , Issue 1 , June 1982 , pp. 116 - 118
Copyright
Copyright © University College London 1982

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References

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