A Note on Invariant Finitely Additive Measures

S. G. Dani
1985 Proceedings of the American Mathematical Society  
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.
doi:10.2307/2044555 fatcat:omsmulkdlbfpxa3z5nzva6uveq