Invariant measures of action of amenable groups and their entropy

Document Type : Original Article

Authors

1 Department of Mathematics, Jundi-Shapur University of Technology, Dezful, Iran

2 Department of Electrical Engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran

Abstract

In this article, with the help of the concept of diagonal measure, we define an information function for the amenable group action on a compact metric space and then obtain the entropy of the group action from it. In other words, we show that the integral of the defined information function will be equal to the entropy of the amenable group action.

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References

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Measure Algebras and Applications
Volume 2, Issue 1 - Serial Number 2
August 2024
Pages 130-141

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History

  • Receive Date: 12 April 2024
  • Revise Date: 17 June 2024
  • Accept Date: 26 June 2024

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