Some functions with a unique invariant mean

Talagrand, Michel

doi:10.1090/S0002-9939-1981-0609661-3

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Some functions with a unique invariant mean
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by Michel Talagrand PDF

Proc. Amer. Math. Soc. 82 (1981), 253-256 Request permission

Abstract:

In a large class of groups, we construct a function which has a unique invariant mean, but which is not Riemann-measurable.

References

Frederick P. Greenleaf, Invariant means on topological groups and their applications, Van Nostrand Mathematical Studies, No. 16, Van Nostrand Reinhold Co., New York-Toronto, Ont.-London, 1969. MR 0251549
L. A. Rubel and A. L. Shields, Invariant subspaces of $L^{\infty }$ and $H^{\infty }$, J. Reine Angew. Math. 272 (1974), 32–44. MR 370156, DOI 10.1090/S0002-9904-1973-13129-5