Simplest General Constructions and Elements of Entropy Theory of Dynamical Systems

Abstract

Consider the measure space (M, 𝔖, μ) which is the Cartesian product of two other measure spaces

$$(M,,\mu ) = ({M_1} \times {M_2},{_1} \times {_2},{\mu _1} \times {\mu _2})$$

Assume that the dynamical systems {T ^t₁ }, {T ^t₂ } act in the factors, either both with discrete time or both with continuous time.