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Equivalence of measure preserving transformations

About this Title

Donald S. Ornstein, Daniel J. Rudolph and Benjamin Weiss

Publication: Memoirs of the American Mathematical Society
Publication Year: 1982; Volume 37, Number 262
ISBNs: 978-0-8218-2262-3 (print); 978-1-4704-0669-1 (online)
DOI: https://doi.org/10.1090/memo/0262
MathSciNet review: 653094
MSC: Primary 28D05; Secondary 28D20

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Table of Contents

Chapters

  • Equivalence
  • 1. Equivalence
  • 2. The $f$-metric
  • 3. Finitely fixed processes
  • 4. The equivalence theorem–I
  • 5. The equivalence theorem–II
  • 6. Loosely Bernoulli transformations
  • 7. Back to flows and skew products
  • 8. Transformations with finite rank
  • Non-equivalence
  • 9. Infinite entropy and various complements
  • 10. Feldman’s example
  • 11. $J^f$ is not isomorphic to $J$
  • 12. $J$ and $J^{-1}$ are not equivalent and uncountably many nonequivalent $0$-entropy transformations
  • 13. Uncountably many pairwise nonequivalent transformations of finite and infinite entropy
  • 14. A loosely Bernoulli $T$ for which $T\times T$ is not loosely Bernoulli