Conditional entropy for Amenable group actions
Yuan Lian, Bin Zhu

TL;DR
This paper defines and explores the properties of conditional entropy for actions of infinite amenable groups on Lebesgue spaces, including a decomposition theorem, advancing the understanding of entropy in this context.
Contribution
It introduces a new definition of conditional entropy for amenable group actions and establishes fundamental properties and a decomposition theorem for this entropy.
Findings
Defined conditional entropy for amenable group actions
Proved properties of the conditional entropy
Established a decomposition theorem for the entropy
Abstract
Let G be an infinite discrete countable amenable group acting continuously on a Lebesgue space X. In this article, using partition and factor-space, the conditional entropy of the action G is defined. We introduction some properties of conditional entropy for amenable group actions and the corresponding decomposition theorem is obtained.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Topological and Geometric Data Analysis · Computability, Logic, AI Algorithms
