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For \(n>3\) there is only one finitely additive rotationally invariant measure on the n-sphere defined on all Lebesgue measurable subsets. (English) Zbl 0459.28009

28C10 Set functions and measures on topological groups or semigroups, Haar measures, invariant measures
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[1] S. Banach, Sur le problème de la mesure, S. Banach Oeuvres, vol I, Warszawa, 1967, pp. 318-322.
[2] D. A. Každan, On the connection of the dual space of a group with the structure of its closed subgroups, Funkcional. Anal. i Priložen. 1 (1967), 71 – 74 (Russian).
[3] Joseph Rosenblatt, Uniqueness of invariant means for measure-preserving transformations, Trans. Amer. Math. Soc. 265 (1981), no. 2, 623 – 636. · Zbl 0464.28008
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