On a geometric property of the set of invariant means on a group
Author:
Ching Chou
Journal:
Proc. Amer. Math. Soc. 30 (1971), 296302
MSC:
Primary 46.80; Secondary 42.00
MathSciNet review:
0283584
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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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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939197102835848
PII:
S 00029939(1971)02835848
Keywords:
Invariant means,
amenable groups,
mean ergodic theorem,
exposed points,
StoneČech compactification
Article copyright:
© Copyright 1971
American Mathematical Society
