Two-step coding theorem in the nearly continuous category
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In measurable dynamics, one studies the measurable properties of dynamical systems. A recent surge of interest has been to study dynamical systems which have both a measurable and a topological structure. A nearly continuous Z-system consists of a Polish space X with a non-atomic Borel probability measure μ and an ergodic measure-preserving homeomorphism T on X . Let ƒ : X → R be a positive, nearly continuous function bounded away from 0 and ∞. This gives rise to a flow built over T under the function ƒ in the nearly continuous category. Rudolph proved a representation theorem in the 1970's, ...