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The Range of Invariant Means on Locally Compact Abelian Groups

Published online by Cambridge University Press:  20 November 2018

Roy C. Snell
Roy C. Snell*
Affiliation:
Department of National Defence, Royal Roads Military College, FMO, Victoria, B.C.
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Abstract

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It has been shown by E. Granirer that for certain infinite amenable discrete groups G there exists a nested family of left almost convergent subsets of G on which every left invariant mean on m(G) attains as its range the entire [0,1] interval. This paper examines the range of left invariant means on L∞(G) for infinite locally compact abelian groups G and demonstrates the existence in every such group of a nested family of left almost convergent Borel subsets on which every left invariant mean on L∞ (G) attains as its range the interval [0,1],

Keywords

43A0728A70
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 4 , 01 December 1974 , pp. 567 - 573
Copyright
Copyright © Canadian Mathematical Society 1974

References

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