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Measures of maximal relative entropy with full support

Published online by Cambridge University Press:  17 November 2010

JISANG YOO
JISANG YOO*
Affiliation:
Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Korea (email: [email protected])
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Abstract

Let π be a factor map from an irreducible shift of finite type X to a shift space Y. Let ν be an invariant probability measure on Y with full support. We show that every measure on X of maximal relative entropy over ν is fully supported. As a result, given any invariant probability measure ν on Y with full support, there is an invariant probability measure μ on X with full support that maps to ν under π. If ν is ergodic, μ can be chosen to be ergodic. These results can be generalized to the case of sofic shifts. We demonstrate that the results do not extend to general shift spaces by providing counterexamples.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 31 , Issue 6 , December 2011 , pp. 1889 - 1899
Copyright
Copyright © Cambridge University Press 2010

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