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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

The exposed points of the set of invariant means


Author: Tianxuan Miao
Journal: Trans. Amer. Math. Soc. 347 (1995), 1401-1408
MSC: Primary 43A07
MathSciNet review: 1260174
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Abstract: Let $ G$ be a $ \sigma $-compact infinite locally compact group, and let $ LIM$ be the set of left invariant means on $ {L^\infty }(G)$. We prove in this paper that if $ G$ is amenable as a discrete group, then $ LIM$ has no exposed points. We also give another proof of the Granirer theorem that the set $ LIM(X,G)$ of $ G$-invariant means on $ {L^\infty }(X,\beta ,p)$ has no exposed points, where $ G$ is an amenable countable group acting ergodically as measure-preserving transformations on a nonatomic probability space $ (X,\beta ,p)$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1995-1260174-2
PII: S 0002-9947(1995)1260174-2
Keywords: Locally compact groups, amenable groups, invariant means, the exposed points
Article copyright: © Copyright 1995 American Mathematical Society