Skip to main content

Advertisement

SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
  1. Home
  2. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
  3. Article
A note on invariant measures for Markov maps of an interval
Download PDF
Download PDF
  • Published: September 1985

A note on invariant measures for Markov maps of an interval

  • Piotr Bugiel1 

Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete volume 70, pages 345–349 (1985)Cite this article

  • 122 Accesses

  • 8 Citations

  • Metrics details

Summary

We present two examples of Markov maps which satisfy the expanding condition, Rényi's condition and do not admit any absolutely continuous invariant measures. These examples are counterexamples to the theorem formulated in [1, p. 1].

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

References

  1. Bowen, R.: Invariant measures for Markov maps of the interval. Commun. Math. Phys. 69, 1–17 (1979)

    Google Scholar 

  2. Bugiel, P.: Approximation for the measures of ergodic transformations of the real line. Z. Wahrscheinlichkeitstheor. Verw. Geb. 59, 27–38 (1982)

    Google Scholar 

  3. Lasota, A., Yorke, J.A.: On the existence of invariant measures for piecewise monotonic transformations. Trans. Am. Math. Soc. 186, 481–488 (1973)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Jagellonian University, Reymonta 4, P-30-059, Kraków, Poland

    Piotr Bugiel

Authors
  1. Piotr Bugiel
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Bugiel, P. A note on invariant measures for Markov maps of an interval. Z. Wahrscheinlichkeitstheorie verw Gebiete 70, 345–349 (1985). https://doi.org/10.1007/BF00534867

Download citation

  • Received: 30 September 1984

  • Issue Date: September 1985

  • DOI: https://doi.org/10.1007/BF00534867

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Keywords

  • Stochastic Process
  • Probability Theory
  • Invariant Measure
  • Mathematical Biology
  • Continuous Invariant Measure
Download PDF

Working on a manuscript?

Avoid the common mistakes

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

167.114.118.210

Not affiliated

Springer Nature

© 2023 Springer Nature