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Transactions of the American Mathematical Society

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ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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The exposed points of the set of invariant means
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by Tianxuan Miao PDF
Trans. Amer. Math. Soc. 347 (1995), 1401-1408 Request permission

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 $(X,\beta ,p)$.
References
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 347 (1995), 1401-1408
  • MSC: Primary 43A07
  • DOI: https://doi.org/10.1090/S0002-9947-1995-1260174-2
  • MathSciNet review: 1260174