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Ergodic group actions with nonunique invariant means


Author: Ching Chou
Journal: Proc. Amer. Math. Soc. 100 (1987), 647-650
MSC: Primary 43A07; Secondary 28D15
DOI: https://doi.org/10.1090/S0002-9939-1987-0894431-7
MathSciNet review: 894431
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Abstract: Let $ M(X,G)$ be the set of $ G$-invariant means on $ {L^\infty }(X,\mathcal{B},P)$, where $ G$ is a countable group acting ergodically as measure preserving transformations on a nonatomic probability space $ (X,\mathcal{B},P)$. We show that if there exists $ \mu \in M(X,G),\mu \ne P$, then $ M(X,G)$ contains an isometric copy of $ \beta N\backslash N$, where $ \beta N\backslash N$ is considered as a subset of $ {({l^\infty })^*}$. This provides an answer to a question raised by J. Rosenblatt in 1981.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1987-0894431-7
Keywords: Invariant means, ergodic group actions, asymptotically invariant sequences
Article copyright: © Copyright 1987 American Mathematical Society

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