Any Two Irreducible Markov Chains Are Finitarily Orbit Equivalent
نویسندگان
چکیده
Two invertible dynamical systems (X,A, μ, T ) and (Y,B, ν, S) where X, Y are metrizable spaces and T , S are homeomorphisms on X and Y , are said to be finitarily orbit equivalent if there exists an invertible measure preserving mapping φ from a subset X0 of X of full measure to a subset Y0 of Y of full measure such that φ|X0 is continuous in the relative topology on X0, φ|Y0 is continuous in the relative topology on Y0 and φ(OrbT (x)) = OrbSφ(x) for μ-a.e. x ∈ X. In this article a finitary orbit equivalence mapping is shown to exist between any two irreducible Markov chains.
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