K-property for Maharam extensions of nonsingular Bernoulli and Markov shifts
Abstract
It is shown that each conservative nonsingular Bernoulli shift is either of type II1 or III1. Moreover, in the latter case the corresponding Maharam extension of the shift is a K-automorphism. This extends earlier results obtained by Z.~Kosloff for the equilibrial shifts. Nonequilibrial shifts of type III1 are constructed. We further generalize (partly) the main results to nonsingular Markov shifts.
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