Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Nonexistence of invariant measures

Author: David Promislow
Journal: Proc. Amer. Math. Soc. 88 (1983), 89-92
MSC: Primary 43A07; Secondary 28C10
MathSciNet review: 691283
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Abstract: Let $ G$ be a group acting on a set $ X$. Suppose that for some positive integer $ r$, $ G$ contains a free group $ F$ of rank $ > r$ and the intersection of any stabilizer with $ F$ has rank $ \leqslant r$. A graph theoretic approach is used to show that there is no invariant measure on $ X$.

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Article copyright: © Copyright 1983 American Mathematical Society