Skip to main content

Approximation and baire category theorems in ergodic theory

  • Conference paper
  • First Online:
Measure Theory and its Applications

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1033))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. AARONSON: On the Categories of Ergodicity when the Measure is Infinite. Ergodic Theory, Proceedings Oberwolfach 1978, Springer Lecture Notes in Math 729 (1979), 1–7.

    Google Scholar 

  2. J. AARONSON: The Asymptotic Distributional Behaviour of Transformations Preserving Infinite Measures. J. d'analyse 39 (1981), 203–234.

    Article  MathSciNet  MATH  Google Scholar 

  3. S. ALPERN: New Proofs that Weak Mixing is Generic. Inventiones Math. 32 (1976), 263–278.

    Article  MathSciNet  MATH  Google Scholar 

  4. S. ALPERN: Approximation to and by Measure Preserving Homeomorphisms. J. London Math. Soc. 18 (1978), 305–315.

    Article  MathSciNet  MATH  Google Scholar 

  5. S. ALPERN: A Topological Analog of Halmos' Conjugacy Lemma. Inventiones Math. 48 (1978), 1–6.

    Article  MathSciNet  MATH  Google Scholar 

  6. S. ALPERN: Generic Properties of Measure Preserving Homeomorphisms. Ergodic Theory, Proceedings Oberwolfach 1978, Springer Lecture Notes in Math. 729 (1979), 16–27.

    Google Scholar 

  7. S. ALPERN: Measure Preserving Homeomorphisms of ℝn. Indiana U. Math. J. 28 (1979), 957–960.

    Article  MathSciNet  MATH  Google Scholar 

  8. S. ALPERN: Return Times and Conjugates of an Antiperiodic Transformation. Ergodic Theory & Dynamical Systems, 1 (1981), 135–143.

    Article  MathSciNet  MATH  Google Scholar 

  9. S. ALPERN: Nonstable Ergodic Homeomorphisms of ℝ4, Indiana U. Math. J. 32 (1983), 187–191.

    Article  MathSciNet  MATH  Google Scholar 

  10. S. ALPERN & R. D. EDWARDS: Lusin's Theorem for Measure Preserving Homeomorphisms. Mathematika 26 (1979), 33–43.

    Article  MathSciNet  MATH  Google Scholar 

  11. J. R. BROWN: Approximation Theorems for Markov Operators. Pacific J. Math. 16 (1966), 13–23.

    Article  MathSciNet  MATH  Google Scholar 

  12. R. V. CHACON: Approximation of Transformations with Continuous Spectrum. Pacific J. Math. 31 (1969), 293–302.

    Article  MathSciNet  MATH  Google Scholar 

  13. R. V. CHACON: Weakly Mixing Transformations which are not Strongly Mixing. Proc. Amer. Math. Soc. 22 (1969), 559–562.

    Article  MathSciNet  MATH  Google Scholar 

  14. R. V. CHACON AND N. A. FRIEDMAN: Approximation and Invariant Measures. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 3 (1965), 286–295.

    Article  MathSciNet  MATH  Google Scholar 

  15. J. R. CHOKSI, J. HAWKINS & V. S. PRASAD: Type III1 Transformations and their Cocycle Extensions. (to appear).

    Google Scholar 

  16. J. R. CHOKSI & S. KAKUTANI: Residuality of Ergodic Measurable Transformations and of Ergodic Transformations which Preserve an Infinite Measure. Indiana U. Math. J. 28 (1979), 453–469.

    Article  MathSciNet  MATH  Google Scholar 

  17. J. R. CHOKSI & V. S. PRASAD: Ergodic Theory on Homogeneous Measure Algebras. Measure Theory Oberwolfach 1981, Proceedings, Springer Lecture Notes in Math. 945 (1982), 366–408.

    Google Scholar 

  18. N. A. FRIEDMAN: Introduction to Ergodic Theory, Van Nostrand Reinhold Studies in Math. No. 29, New York, 1970.

    Google Scholar 

  19. P. R. HALMOS: Measure Theory. D. Van Nostrand, New York 1950; reprinted Springer, New York, 1975.

    Book  MATH  Google Scholar 

  20. P.R. HALMOS: Lectures on Ergodic Theory. Publ. Math. Soc. Japan, Tokyo 1956; reprinted Chelsea, New York 1960.

    MATH  Google Scholar 

  21. P. R. HALMOS: Approximation Theories for Measure Preserving Transformations. Trans. Amer. Math. Soc. 55 (1944), 1–18.

    Article  MathSciNet  MATH  Google Scholar 

  22. P. R. HALMOS: In General a Measure Preserving Transformation is Mixing. Ann. of Math. 45 (1944), 786–792.

    Article  MathSciNet  MATH  Google Scholar 

  23. A. IONESCU TULCEA: On the Category of Certain Classes of Transformations in Ergodic Theory. Trans. Amer. Math. Soc. 114 (1965), 261–279.

    Article  MathSciNet  MATH  Google Scholar 

  24. A. IWANIK: Approximation Theorems for Stochastic Operators. Indiana U. Math. J. 29 (1980), 415–425.

    Article  MathSciNet  MATH  Google Scholar 

  25. A. DEL JUNCO: Disjointness of Measure Preserving Transformations, Minimal Self-Joinings and Category. Ergodic Theory and Dynamical Systems I, Proceedings Special Year, Maryland 1979–80, Progress in Math. 10, Birkhauser, Boston, 1981, 81–89.

    Google Scholar 

  26. S. KAKUTANI: Induced Measure Preserving Transformations. Proc. Imperial Acad. Tokyo 19 (1943), 635–641.

    Article  MathSciNet  MATH  Google Scholar 

  27. S. KAKUTANI & W. PARRY: Infinite Measure Preserving Transformations with "Mixing". Bull. Amer. Math. Soc 69 (1963), 752–756.

    Article  MathSciNet  MATH  Google Scholar 

  28. A.B. KATOK & E.A. ROBINSON: Constructions in Ergodic Theory. (To appear).

    Google Scholar 

  29. A. B. KATOK & A.M. STEPIN: Approximations in Ergodic Theory (Russian). Uspekhi Math. Nauk 22 (1967), 81–106; translated in Russian Math. Surveys 22 (1967), 77–102.

    MathSciNet  MATH  Google Scholar 

  30. A. B. KATOK & A. M. STEPIN: Metric Properties of Measure Preserving Homeomorphisms (Russian). Uspekhi Math. Nauk 25 (1970), 193–220; translated in Russian Math. Surveys 25 (1970), 191–220.

    MathSciNet  MATH  Google Scholar 

  31. U. KRENGEL: Entropy of Conservative Transformations. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 7 (1966), 161–181.

    Article  MathSciNet  MATH  Google Scholar 

  32. U. KRENGEL & L. SUCHESTON: On Mixing in Infinite Measure Spaces. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 13 (1969), 150–164.

    Article  MathSciNet  MATH  Google Scholar 

  33. K. KRICKEBERG: Mischende Transformationen auf Mannigfaltigkeiten Unendlichen Masses. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 7 (1967), 235–247.

    Article  MathSciNet  MATH  Google Scholar 

  34. J. C. OXTOBY: Approximation by Measure Preserving Homeomorphisms. Recent Advances in Topological Dynamics, Proc. of Conf. in honour of G. A. Hedlund at Yale U. June 1972, Springer, Lecture Notes in Math. 318 (1973), 206–217.

    Google Scholar 

  35. J. C. OXTOBY & V. S. PRASAD: Homeomorphic Measures in the Hilbert Cube. Pacific J. Math. 77 (1978), 483–497.

    Article  MathSciNet  MATH  Google Scholar 

  36. J. C. OXTOBY & S. M. ULAM: Measure Preserving Homeomorphisms and Metrical Transitivity. Ann. of Math. 42 (1941), 874–920.

    Article  MathSciNet  MATH  Google Scholar 

  37. V. S. PRASAD: Ergodic Measure Preserving Homeomorphisms of Rn, Indiana U. Math. J. 28 (1979), 859–867.

    Article  MATH  Google Scholar 

  38. V. S. PRASAD: A Mapping Theorem for Hilbert Cube Manifolds. Proc. Amer. Math. Soc. (to appear).

    Google Scholar 

  39. V. S. PRASAD: Generating Dense Subgroups of Measure Preserving Transformations. Proc. Amer. Math. Soc. 83 (1981), 286–288.

    Article  MathSciNet  MATH  Google Scholar 

  40. V. S. PRASAD: Sous-groupes libres et sous-ensembles indépendants, de transformations préservant la mesure. Proceedings of the Workshop on Measure Theory and its Applications (Sherbrooke, 1982), Lecture Notes in Mathematics, Springer-Verlag.

    Google Scholar 

  41. V. A. ROHLIN: A General Measure Preserving Transformation is not Mixing (Russian). Doklady Akad. Nauk S.S.S.R. (N.S.) 60 (1948), 349–351.

    MathSciNet  Google Scholar 

  42. V. A. ROHLIN: Selected Problems in the Metric Theory of Dynamical Systems (Russian). Uspekhi Math. Nauk, 30 (1949), 57–128; translated in Amer. Math. Soc. Translations (2) 49 (1966), 171–240.

    MathSciNet  Google Scholar 

  43. V. A. ROHLIN: Entropy of Metric Endomorphisms (Russian). Doklady Akad. Nauk S.S.S.R. (N.S.) 124 (1959), 980–983.

    MathSciNet  Google Scholar 

  44. U. SACHDEVA: On Category of Mixing in Infinite Measure Spaces. Math. Systems Theory 5 (1971), 319–330.

    Article  MathSciNet  MATH  Google Scholar 

  45. H. E. WHITE Jr.: The Approximation of one-one Measurable Transformations by Measure Preserving Homeomorphisms. Proc. Amer. Math. Soc. 44 (1974), 391–394.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Jean-Marc Belley Jacques Dubois Pedro Morales

Rights and permissions

Reprints and permissions

Copyright information

© 1983 Springer-Verlag

About this paper

Cite this paper

Choksi, J.R., Prasad, V.S. (1983). Approximation and baire category theorems in ergodic theory. In: Belley, JM., Dubois, J., Morales, P. (eds) Measure Theory and its Applications. Lecture Notes in Mathematics, vol 1033. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099849

Download citation

  • DOI: https://doi.org/10.1007/BFb0099849

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12703-1

  • Online ISBN: 978-3-540-38690-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics