Measures of maximal entropy

Subject Areas : Abstract harmonic analysis

M. Amini ¹ (Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran 14115-134, Iran)

Received: 2019-02-28 Accepted : 2019-03-17 Published : 2019-12-01

Keywords: locally compact group, Infinite invariant measure, Haar measure, maximal entropy,

Abstract :

We extend the results of Walters on the uniqueness of invariant measures with maximal entropy on compact groups to an arbitrary locally compact group. We show that the maximal entropy is attained at the left Haar measure and the measure of maximal entropy is unique.

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