Álgebra de Pinsker e a propriedade K

Abstract

In this work, we study the ergodic theoretical notions of Pinsker Algebra and the K Property, stressing the relationship between these two concepts. More specifically, our goal is to establish, via the Pinsker Algebra, necessary and sufficient conditions for an automorphism to be K. We also prove that the K property is equivalent to K-mixing. Firstly, we study the metric entropy of finite and countable partitions and, later, we consider the metric entropy involving measurable partitions. Later, we use the notion of metric entropy to define and characterize the Pinsker algebra. Finally, we study the K property, presenting a characterization in terms of the Pinsker algebra, as well as equivalent definitions, and we also present three classical examples of K-automorphisms.