A note on invariant finitely additive measures

Dani, S. G.

doi:10.1090/S0002-9939-1985-0766529-3

A note on invariant finitely additive measures
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by S. G. Dani PDF

Proc. Amer. Math. Soc. 93 (1985), 67-72 Request permission

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.

References

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Algebraische Fassung des Massproblems

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