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I am looking for a reference of the proof that a Markov shift is pointwise dual ergodic, I tried google it but with no success.

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  • $\begingroup$ Yes, the transition matrix is irreducible and recurrent. $\endgroup$
    – Alan
    Commented Dec 5, 2014 at 7:46
  • $\begingroup$ For this case, we have use some argument of the spectrum analysis of primitive matrix, I think the good book for beginner is Peter Walters' an introduction to ergodic theory. $\endgroup$
    – yaoxiao
    Commented Dec 5, 2014 at 7:48
  • $\begingroup$ On which pages does he discuss this topic? $\endgroup$
    – Alan
    Commented Dec 5, 2014 at 7:49
  • $\begingroup$ I was looking at Walters' book, he doesn't discuss over there the topic of pointwise dual ergodicity. $\endgroup$
    – Alan
    Commented Dec 5, 2014 at 7:56
  • $\begingroup$ Sorry, an introduction to infinite ergodic theory page 126. $\endgroup$
    – yaoxiao
    Commented Dec 5, 2014 at 8:02

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