Reference for Markov chains that uses ergodic theory definition of ergodic

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I'm looking for a reference on Markov chains that at least handles discrete time, countable state space (not just finite state space), that uses the ergodic theory definition of ergodic (shift operator is ergodic measurable transformation) instead of the more common probability definition (irreducible, aperiodic, positive recurrent). Can you recommend one or more references?