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Measure-theoretic pressure for amenable group actions

Volume 148 / 2017

Yun Zhao Colloquium Mathematicum 148 (2017), 87-106 MSC: Primary 37D35; Secondary 37A60, 43A07. DOI: 10.4064/cm6784-6-2016 Published online: 24 February 2017


This paper defines measure-theoretic pressure for an amenable group action by using spanning sets, and shows that the measure-theoretic pressure of an ergodic measure can be described in terms of metric entropy and an integral of the observable associated with the ergodic measure. Using the theory of Carathéodory structure, we give an equivalent definition of measure-theoretic pressure for amenable group actions, and obtain an inverse variational principle, i.e., the topological pressure on a certain set is exactly the measure-theoretic pressure of an ergodic measure.


  • Yun ZhaoDepartment of Mathematics
    Soochow University
    Suzhou 215006, China

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