In addition to the class notes, see also [HK] sections 7.3.4-7.3.7 for a treatment of topological Markov chains. The notes in [HK] consider predominantly invertible (two-sided) shifts on bi-infinite sequences of finite numbers of symbols instead of the non-invertible (one-sided) shift on semi-infinite sequences that we have been considering in the lectures. But both treatments are very similar and all the statements in [HK] section 7.3.7 equally hold for the one-sided shift.
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