Invariant measures of action of amenable groups and their entropy

doi
10.22091/maa.2024.10600.1018
چکیده

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.