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Lacunary isomorphism of decreasing sequences of measurable partitions

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Abstract

The lacunary and orbital isomorphism problem is solved for a wide class of decreasing sequences of measurable partitions of Lebesgue spaces which are finitely isomorphic to the standard Bernoulli sequences.

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References

  1. L. Dubins, J. Feldman, M. Smorodinsky and B. Tsirelson,Confiltrations and measure change for Brownian motion, Preprint, 1994.

  2. H. Dye,On groups of measure preserving transformations. I, American Journal of Mathematics81 (1959), 119–159.

    Article  MATH  MathSciNet  Google Scholar 

  3. H. Dye,On groups of measure preserving transformations. II, American Journal of Mathematics85 (1963), 551–576.

    Article  MATH  MathSciNet  Google Scholar 

  4. J. Feldman and C.C. Moore,Ergodic equivalence relations, cohomology and von Neumann algebras. I.II, Transactions of the American Mathematical Society234 (1977), 289–324, 325–361.

    Article  MATH  MathSciNet  Google Scholar 

  5. O. Guseva,Classification of sequences of measurable partitions, Vestnik LGU1 (1965), 14–23.

    MathSciNet  Google Scholar 

  6. W. Krieger,On non-singular transformations of a measure space. I, Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete11 (1969), 83–97.

    Article  Google Scholar 

  7. W. Krieger,On non-singular transformations of a measure space. II, Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete11 (1969), 98–119.

    Article  MathSciNet  Google Scholar 

  8. W. Krieger,On ergodic flows and the isomorphism of factors, Mathematische Annalen223 (1976), 19–70.

    Article  MATH  MathSciNet  Google Scholar 

  9. V. Rokhlin,On the fundamental ideas of the measure theory, Matematicheskii Sbornik25 (1949), 107–150 (Russian); American Mathematical Society Translations71 (1952), 1–54.

    Google Scholar 

  10. V. Rokhlin,Lectures on the entropy theory of transformations with invariant measure, Uspekhi Matematicheskikh Nauk22 (1967), 3–56 (Russian); Russian Mathematical Surveys22 (1967), 1–52.

    Google Scholar 

  11. B. Rubshtein,On decreasing sequences of measurable partitions, Soviet Mathematics Doklady13 (1972), 962–965.

    Google Scholar 

  12. B. Rubshtein,On sequences of measurable partitions generated by endomorphisms of Lebesgue space, Uspekhi Matematicheskikh Nauk28 (1973), 247–248.

    Google Scholar 

  13. B. Rubshtein,On absolutely non-homogeneous sequences of measurable partitions, inStochastic Processes and Statistical Inferences, Tashkent FAN3 (1973), 156–164.

    Google Scholar 

  14. B. Rubshtein,Non-homogeneous finitely Bernoulli sequences of measurable partitions, Functional Analysis and its Applications10 (1976), 39–44.

    Article  Google Scholar 

  15. A. Stepin,On an entropy invariant of decreasing sequences of measurable partitions, Functional Analysis and its Applications5 (1976), 80–84.

    MathSciNet  Google Scholar 

  16. A. Vershik,A lacunary isomorphism theorem for monotone sequences of partitions, Functional Analysis and its Applications2 (1968), 17–21.

    MATH  Google Scholar 

  17. A. Vershik,Decreasing sequences of measurable partitions and their applications, Soviet Mathematics Doklady11 (1970), 1007–1011.

    MATH  Google Scholar 

  18. A. Vershik,A continuum of pairwise non-isomorphic dyadic sequences, Functional Analysis and its Applications5 (1971), 16–18.

    MathSciNet  Google Scholar 

  19. V. Vinokurov and N. Gonikhodzaev,Conditional functions in trajectory theory of dynamical systems, Izvestiya Akademii Nauk SSSR42 (1978), 428–463.

    Google Scholar 

  20. V. Vinokurov, B. Rubshtein and A. Fedorov,Lebesgue space and their measurable partitions, Tashkent University 1985, 75pp (Russian).

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Correspondence to Ben-Zion Rubshtein.

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Rubshtein, BZ. Lacunary isomorphism of decreasing sequences of measurable partitions. Isr. J. Math. 97, 317–345 (1997). https://doi.org/10.1007/BF02774044

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  • DOI: https://doi.org/10.1007/BF02774044

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