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arXiv · 2004.05781

On Absolutely Continuous Invariant Measures and Krieger-Type of Markov Subshifts

Nachi Avraham-Re'em
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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 $\mathrm{III}_1$. A criterion for equivalence of Markov measures is included.

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Nachi Avraham-Re'em. 2020-04-13. On Absolutely Continuous Invariant Measures and Krieger-Type of Markov Subshifts. https://doi.org/10.1007/s11854-022-0217-4

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