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An entropy equidistribution property for a measurable partition under the action of an amenable group
Author:
J. C. Kieffer
Journal:
Bull. Amer. Math. Soc. 81 (1975), 464-466
MSC (1970):
Primary 60F99, 28A65; Secondary 43A07
MathSciNet review:
0361003
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References |
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Additional Information
- 1.
Jacqueline
Chatard, Applications des propriétés de moyenne
d’un groupe localement compact à la théorie
ergodique, Ann. Inst. H. Poincaré Sect. B (N.S.)
6 (1970), 307–326; erratum, ibid. (N.S.) 7 (1971),
81–82 (French, with English summary). MR 0297965
(45 #7017)
- 2.
J.
P. Conze, Entropie d’un groupe abélien de
transformations, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete
25 (1972/73), 11–30 (French). MR 0335754
(49 #534)
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Frederick
P. Greenleaf, Invariant means on topological groups and their
applications, Van Nostrand Mathematical Studies, No. 16, Van Nostrand
Reinhold Co., New York-Toronto, Ont.-London, 1969. MR 0251549
(40 #4776)
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Yitzhak
Katznelson and Benjamin
Weiss, Commuting measure-preserving transformations, Israel J.
Math. 12 (1972), 161–173. MR 0316680
(47 #5227)
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A.
A. Kirillov, Dynamical systems, factors and group
representations, Uspehi Mat. Nauk 22 (1967),
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(36 #347)
- 6.
Donald
Ornstein, Bernoulli shifts with the same entropy are
isomorphic, Advances in Math. 4 (1970), 337–352
(1970). MR
0257322 (41 #1973)
- 7.
B.
S. Pickel′ and A.
M. Stepin, The property of the entropy equidistribution of
commutative groups of metric automorphisms, Dokl. Akad. Nauk SSSR
198 (1971), 1021–1024 (Russian). MR 0304615
(46 #3750)
- 8.
Jean-Paul
Thouvenot, Convergence en moyenne de l’information pour
l’action de 𝑍², Z. Wahrscheinlichkeitstheorie und
Verw. Gebiete 24 (1972), 135–137 (French). MR 0321612
(47 #10145)
- 1.
- J. Chatard, Applications des propriétés de moyenne d'un groupe localement compact à la théorie ergodique, Ann. Inst. H. Poincaré Sect. B 6 (1970), 307-326; erratum, ibid. 7 (1971), 81-82. MR 45 #7017. MR 297965
- 2.
- J. P. Conze, Entropie d'un groupe abelian de tranformations, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 25 (1972), 11-30. MR 335754
- 3.
- F. P. Greenleaf, Invariant means on topological groups and their applications, Van Nostrand Math. Studies, no. 16, Van Nostrand, New York, 1969. MR 40 #4776. MR 251549
- 4.
- Y. Katznelson and B. Weiss, Commuting measure-preserving transformations, Israel J. Math 12 (1972), 161-173. MR 47 #5227. MR 316680
- 5.
- A. A. Kirillov, Dynamical systems, factors and group representations, Uspehi Mat. Nauk 22 (1967), no. 5 (137), 67-80 = Russian Math. Surveys 22 (1967), 63-75. MR 36 #347. MR 217256
- 6.
- D. Ornstein, Bernoulli shifts with the same entropy are isomorphic, Advances in Math. 4 (1970), 337-352. MR 41 #1973. MR 257322
- 7.
- B. S. Pickel' and A. M. Stepin, The property of the entropy equidistribution of commutative groups of metric automorphisms, Dokl. Akad. Nauk SSSR 198 (1971), 1021-1024 = Soviet Math. Dokl. 12 (1971), 938-942. MR 46 #3750. MR 304615
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- J. P. Thouvenot, Convergence en moyenne de l'information pour l'action de Z2, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 24 (1972), 135-137. MR 321612
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9904-1975-13786-4
PII:
S 0002-9904(1975)13786-4
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