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.
Citation
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
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