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MARKOV SHIFTS SUPPORTED ON TOPOLOGICAL MARKOV SHIFTS

We construct inhomogenous Markov measures for which the shift is of Kreiger type III1. These measures are fully supported on a toplogical Markov shift space of the hyperbolic toral automorphism f(x, y) = ({x + y}, x) : T → T and are used in a subsequent paper [Kos1] in the construction of C Anosov diffeomorphisms of T without an absolutely continuous invariant measure.