Skip to main content

The Poincaré Recurrence Lemma

  • Chapter
Basic Ergodic Theory

Part of the book series: Texts and Readings in Mathematics ((TRM,volume 6))

Abstract

Let X be a non-empty set. A σ-algebra Ɓ on X is a non-empty collection of subsets of X which is closed under countable unions and complements. A set together with a σ-algebra Ɓ is called a Borel space or a Borel structure (X, Ɓ).

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 40.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

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. G. D. Birkhoff. Recent Advances in Dynamics, Science, January 16, 1920, vol. 51, no. 1307, 51–55. Birkhoff: Collected Mathematical Papers, vol. 2, 106–110, Dover, 1968.

    Article  Google Scholar 

  2. G. D. Birkhoff and B. O. Koopman. Recent Contributions to Ergodic Theory. Proc. Nat. Acad. Sci. U. S. A., 18 (1932), 279–282. Birkhoff: Collected Mathematical Papers, vol. 2, 462–465, Dover, 1968.

    Article  MATH  Google Scholar 

  3. C. Carathéodory. Über den Wiederkehrsatz von Poincaré., Preüuss. Acad. Wiss. 34(1919), 580–584)

    MATH  Google Scholar 

  4. H. Furstenberg. Recurrence in Ergodic Theory and Combinatorial Number Theory. Princeton University Press, 1981.

    Book  MATH  Google Scholar 

  5. K. R. Parthasarathy. Probability Measures on Metric Spaces. American Mathematical Society, 2004.

    MATH  Google Scholar 

  6. J. C. Oxtoby. Measure and Category. Springer-Verlag, 1980.

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Hindustan Book Agency

About this chapter

Cite this chapter

Nadkarni, M.G. (2013). The Poincaré Recurrence Lemma. In: Basic Ergodic Theory. Texts and Readings in Mathematics, vol 6. Hindustan Book Agency, Gurgaon. https://doi.org/10.1007/978-93-86279-53-8_1

Download citation

Publish with us

Policies and ethics