Geodesic
An invariant of monotone equivalence determining the quotients of automorphisms monotonely equivalent to a~Bernoulli shift
Izvestiya. Mathematics , Tome 11 (1977) no. 1, pp. 147-169.

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Two ergodic automorphisms of a Lebesgue space are called monotonely equivalent if they have metrically isomorphic induced automorphisms. We formulate properties of an automorphism of a Lebesgue space, similar to very weak Bernoulli and finitely determined. The difference is that instead of the Hamming metric on the space of words, we use a weaker metric $\rho^M$. These properties describe the class of quotient automorphisms of automorphisms monotonely equivalent to Bernoulli shifts. Bibliography: 12 titles. 
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E. A. Sataev. An invariant of monotone equivalence determining the quotients of automorphisms monotonely equivalent to a~Bernoulli shift. Izvestiya. Mathematics , Tome 11 (1977) no. 1, pp. 147-169. http://geodesic.mathdoc.fr/item/IM2_1977_11_1_a4/

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