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December, 1975 A Generalized Shannon-McMillan Theorem for the Action of an Amenable Group on a Probability Space
J. C. Kieffer
Ann. Probab. 3(6): 1031-1037 (December, 1975). DOI: 10.1214/aop/1176996230

Abstract

A generalization of the Shannon-McMillan Theorem ($L^1$ version) is obtained for the action of an amenable group on a probability space, thereby settling a conjecture of Pickel and Stepin. Interesting properties of the limit function are derived. The entropy of an action of an amenable group is defined.

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J. C. Kieffer. "A Generalized Shannon-McMillan Theorem for the Action of an Amenable Group on a Probability Space." Ann. Probab. 3 (6) 1031 - 1037, December, 1975. https://doi.org/10.1214/aop/1176996230

Information

Published: December, 1975
First available in Project Euclid: 19 April 2007

zbMATH: 0322.60032
MathSciNet: MR393422
Digital Object Identifier: 10.1214/aop/1176996230

Subjects:
Primary: 60F99
Secondary: ‎43A07‎

Keywords: ‎amenable group , Entropy , group action , partition of a probability space , Shannon-McMillan theorem

Rights: Copyright © 1975 Institute of Mathematical Statistics

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Vol.3 • No. 6 • December, 1975
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