On a geometric property of the set of invariant means on a group

Author:
Ching Chou

Journal:
Proc. Amer. Math. Soc. **30** (1971), 296-302

MSC:
Primary 46.80; Secondary 42.00

MathSciNet review:
0283584

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Abstract | References | Similar Articles | Additional Information

Abstract: If *G* is a discrete group and then denotes the homeomorphism of onto induced by left multiplication by *x*. A subset *K* of is said to be *invariant* if it is closed, nonempty and for each . Let denote the set of left invariant means on *G*. (They can be considered as measures on .)

*Let G be a countably infinite amenable group and let K be an invariant subset of* . *Then the nonempty* -*compact convex set* *has no exposed points (with respect to* -*topology*). *Therefore, it is infinite dimensional*.

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1971-0283584-8

Keywords:
Invariant means,
amenable groups,
mean ergodic theorem,
exposed points,
Stone-Čech compactification

Article copyright:
© Copyright 1971
American Mathematical Society