For 𝑛>3 there is only one finitely additive rotationally invariant measure on the 𝑛-sphere defined on all Lebesgue measurable subsets

Sullivan, Dennis

doi:10.1090/S0273-0979-1981-14880-1

Bulletin of the American Mathematical Society

Published by the American Mathematical Society, the Bulletin of the American Mathematical Society (BULL) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.47.

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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
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Bull. Amer. Math. Soc. 4 (1981), 121-123

References

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). MR 0209390
Joseph Rosenblatt, Uniqueness of invariant means for measure-preserving transformations, Trans. Amer. Math. Soc. 265 (1981), no. 2, 623–636. MR 610970, DOI 10.1090/S0002-9947-1981-0610970-7