Skip to main content
SpringerLink
Log in

A criterion for a process to be prime

  • Published:
Monatshefte für Mathematik Aims and scope Submit manuscript

Abstract

A criterion for a measure preserving transformation to be “prime” is given. The criterion allows the transformation to have uncountable centralizer.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Chacón, R. V.: Weakly mixing transformations which are not strongly mixing. Proc. Amer. Math. Soc.22, 559–562 (1969).

    Google Scholar 

  2. Furstenberg, H.: Ergodic behaviour of diagonal measures and a theorem of Szemerédi on arithmetic progressions. J. d'Analyse Math.31, 204–256 (1977).

    Google Scholar 

  3. Halmos, P. R.: Lectures on Ergodic Theory. New York: Chelsea. 1960.

    Google Scholar 

  4. Del Junco, A.: A family of counterexamples in ergodic theory. Preprint. 1981.

  5. Del Junco, A.: A simple measure-preserving transformation with trivial centralizer. Pacific J. Math.79, 357–362 (1978).

    Google Scholar 

  6. Del Junco, A., Rahe, M., Swanson, L.: Chacon's automorphism has minimal self-joinings. J. d'Analyse Math.37, 276–284 (1980).

    Google Scholar 

  7. Ornstein, D. S.: On the root problem in ergodic theory. In: Proc. Sixth Berkeley Symp. Math. Stat. Prob., Vol. II, pp. 347–356. University of California Press. 1967.

  8. Rudolph, D.: An example of a measure-preserving map with minimal self-joinings, and applications. J. d'Analyse Math.35, 97–122 (1979).

    Google Scholar 

  9. Veech, W. A.: Gauss measures for transformations on the space of interval exchange maps. Annals Math.115, 201–242 (1982).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Rice University, P.O. Box 1892, 77251, Houston, TX, USA

    William A. Veech

Authors
  1. William A. Veech
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research supported by NSF-MCS-80-26540.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Veech, W.A. A criterion for a process to be prime. Monatshefte für Mathematik 94, 335–341 (1982). https://doi.org/10.1007/BF01667386

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01667386

Keywords

Search

Navigation