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 
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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Voir la notice de l'article provenant de la source Math-Net.Ru

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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[7] Sataev E. A., “Invariant monotonnoi ekvivalentnosti, opredelyayuschii faktory ot avtomorfizmov, monotonno ekvivalentnykh sdvigu Bernulli”, Chetvertyi Mezhdunarodnyi simpozium po teorii informatsii, Tezisy dokladov, ch. I, M., L., 1976

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[9] Katok A. B., “Monotonnaya ekvivalentnost v ergodicheskoi teorii”, Izv. AN SSSR. Ser. matem., 41 (1977), 104–157 | MR | Zbl

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[11] Friedman N. A., Ornstein D. S., “Ergodic Transformations Induce Mixing Transformations”, Adv. Math., 10:1 (1973), 147–163 | DOI | MR | Zbl

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