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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

A note on invariant finitely additive measures


Author: S. G. Dani
Journal: Proc. Amer. Math. Soc. 93 (1985), 67-72
MSC: Primary 28C10; Secondary 22D40, 43A05
MathSciNet review: 766529
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Abstract: We show that under certain general conditions any finitely additive measure which is defined for all subsets of a set $ X$ and is invariant under the action of a group $ G$ acting on $ X$ is concentrated on a $ G$-invariant subset $ Y$ on which the $ G$-action factors to that of an amenable group. The result is then applied to prove a conjecture of $ S$. Wagon about finitely additive measures on spheres.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0766529-3
PII: S 0002-9939(1985)0766529-3
Keywords: Invariant finitely additive measures, amenable groups
Article copyright: © Copyright 1985 American Mathematical Society