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.
Publié le : 1975-12-14
Classification:
Amenable group,
Shannon-McMillan theorem,
entropy,
group action,
partition of a probability space,
60F99,
43A07
@article{1176996230,
author = {Kieffer, J. C.},
title = {A Generalized Shannon-McMillan Theorem for the Action of an Amenable Group on a Probability Space},
journal = {Ann. Probab.},
volume = {3},
number = {6},
year = {1975},
pages = { 1031-1037},
language = {en},
url = {http://dml.mathdoc.fr/item/1176996230}
}
Kieffer, J. C. A Generalized Shannon-McMillan Theorem for the Action of an Amenable Group on a Probability Space. Ann. Probab., Tome 3 (1975) no. 6, pp. 1031-1037. http://gdmltest.u-ga.fr/item/1176996230/