Journal
JOURNAL OF FUNCTIONAL ANALYSIS
Volume 261, Issue 4, Pages 1028-1082Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jfa.2011.04.014
Keywords
Entropy; Amenable group; Variational principle; Entropy tuple
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Funding
- NSFC [10911120388, 11071231, 10801035]
- Fok Ying Tung Education Foundation
- Fundamental Research Funds for the Central Universities
- FANEDD [201018]
- Chinese Ministry of Education [200802461004]
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The local properties of entropy for a countable discrete amenable group action are studied. For such an action, a local variational principle for a given finite open cover is established, from which the variational relation between the topological and measure-theoretic entropy tuples is deduced. While doing this it is shown that two kinds of measure-theoretic entropy for finite Borel covers coincide. Moreover, two special classes of such an action: systems with uniformly positive entropy and completely positive entropy are investigated. (c) 2011 Elsevier Inc. All rights reserved.
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