Skip to main content

Recent results on mixing in topological measure spaces

  • Conference paper
  • First Online:
Probability and Information Theory

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 89))

  • 768 Accesses

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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.

Bibliography

  1. Böge, W., Krickeberg, K., and F. Papangelou: Über die dem Lebesgueschen Maß isomorphen topologischen Maße. To appear.

    Google Scholar 

  2. Kai Lai Chung and P. Erdös: Probability limit theorems assuming only the first moment. Mem. Amer. Math. Soc. 6, 1–19 (1951).

    MathSciNet  MATH  Google Scholar 

  3. Gillis, J.: Centrally biased discrete random walk. Quart. J. Math. Oxford Ser. (2) 7, 144–152 (1956).

    MathSciNet  MATH  Google Scholar 

  4. Hajian, A. B. and S. Kakutani: Weakly wandering sets and invariant measures. Trans. Amer. Math. Soc. 110, 136–151 (1964).

    Article  MathSciNet  MATH  Google Scholar 

  5. Hopf, E.: Ergodentheorie. Berlin 1937.

    Google Scholar 

  6. Kakutani, S. and W. Parry: Infinite measure preserving transformations with “mixing”. Bull. Amer. Math. Soc. 69, 752–756 (1963).

    Article  MathSciNet  MATH  Google Scholar 

  7. Kemeny, J. G.: A probability limit theorem requiring no moments. Proc. Amer. Math. Soc. 10, 607–612 (1959).

    Article  MathSciNet  MATH  Google Scholar 

  8. Kingman, J. F. C. and S. Orey: Ratio limit theorems for Markov chains. Proc. Amer. Math. Soc. 15, 907–910 (1964).

    Article  MathSciNet  MATH  Google Scholar 

  9. Krickeberg, K.: Strong mixing properties of Markov chains with infinite invariant measure. Proc. Fifth Berkeley Symp. Math. Statist. Probability, Berkeley and Los Angeles 1966, Vol. I, Part II, 431–446.

    Google Scholar 

  10. Krickeberg, K.: Mischende Transformationen auf Mannigfaltigkeiten unendlichen Maßes. Z. Wahrscheinlichkeitstheorie verw. Gebiete 7, 235–247 (1967).

    Article  MathSciNet  MATH  Google Scholar 

  11. Papangelou, F.: Strong ratio limits, R-recurrence and mixing properties of discrete parameter Markov processes. Z. Wahrscheinlichkeitstheorie verw. Gebiete 8, 259–297 (1967).

    Article  MathSciNet  MATH  Google Scholar 

  12. Pruitt, W. E.: Strong ratio limit property for R-recurrent Markov chains. Proc. Amer. Math. Soc. 16, 196–200 (1965).

    MathSciNet  MATH  Google Scholar 

  13. Vere-Jones, D.: Geometric ergodicity in denumerable Markov chains. Quart. J. Math. Oxford Ser. 2, 13, 7–28 (1962).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

M. Behara K. Krickeberg J. Wolfowitz

Rights and permissions

Reprints and permissions

Copyright information

© 1969 Springer-Verlag

About this paper

Cite this paper

Krickeberg, K. (1969). Recent results on mixing in topological measure spaces. In: Behara, M., Krickeberg, K., Wolfowitz, J. (eds) Probability and Information Theory. Lecture Notes in Mathematics, vol 89. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0079125

Download citation

  • DOI: https://doi.org/10.1007/BFb0079125

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-04608-0

  • Online ISBN: 978-3-540-36098-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics