Nonexistence of invariant measures

Promislow, David

doi:10.1090/S0002-9939-1983-0691283-1

Nonexistence of invariant measures
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by David Promislow

Proc. Amer. Math. Soc. 88 (1983), 89-92

DOI: https://doi.org/10.1090/S0002-9939-1983-0691283-1

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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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