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A Generalized Shannon-McMillan Theorem for the Action of an Amenable Group on a Probability Space
J. C. Kieffer
The Annals of Probability
Vol. 3, No. 6 (Dec., 1975), pp. 1031-1037
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/2959209
Page Count: 7
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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.
The Annals of Probability © 1975 Institute of Mathematical Statistics