On Absolutely Continuous Invariant Measures and Krieger-Type of Markov Subshifts
Abstract
It is shown that for a non-singular conservative shift on a topologically mixing Markov subshift with Doeblin Condition the only possible absolutely continuous shift-invariant measure is a Markov measure. Moreover, if it is not equivalent to a homogeneous Markov measure then the shift is of Krieger-type III1. A criterion for equivalence of Markov measures is included.
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