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A counter-example to Dye's Theorem for all non-separable measure algebras
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  • Published: June 1986

A counter-example to Dye's Theorem for all non-separable measure algebras

  • S. J. Eigen1 

Probability Theory and Related Fields volume 72, pages 471–475 (1986)Cite this article

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Summary

In 1959, H. Dye showed that any two ergodic, measure-preserving automorphisms of a Lebesgue measure algebra were weakly equivalent. In this paper, we study weak equivalence, for ergodic measure-preserving automorphisms on non-separable measure algebras. It is shown that, in general, Dye's Theorem does not hold, and in particular, it holds only on separable, i.e. Lebesgue, measure algebras.

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References

  1. Choksi, J.R., Eigen, S.J.: An Automorphism of a Homogeneous Measure Algebra Which Does Not Factorize into a Direct Product, Conference in Modern Analysis and Probability, Contempory Mathematics vol. 26, A.M.S., Providence, 1982

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Authors and Affiliations

  1. Department of Mathematics, Northeastern University, 360 Huntington Avenue, 02115, Boston, MA, USA

    S. J. Eigen

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  1. S. J. Eigen
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Eigen, S.J. A counter-example to Dye's Theorem for all non-separable measure algebras. Probab. Th. Rel. Fields 72, 471–475 (1986). https://doi.org/10.1007/BF00334197

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  • Received: 11 April 1985

  • Issue Date: June 1986

  • DOI: https://doi.org/10.1007/BF00334197

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Keywords

  • Stochastic Process
  • Probability Theory
  • Statistical Theory
  • Lebesgue Measure
  • Measure Algebra
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