Skip to main content
SpringerLink
Log in

The Shannon-McMillan-Breiman theorem for a class of amenable groups

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

Abstract

We prove the SMB theorem for amenable groups that possess Følner sets {A n } with the property that for some constantM, and all,n, |A −1 n A n | ≦M· |A n |.

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.

Institutional subscriptions

Similar content being viewed by others

References

  1. T. Bewley,Extension of the Birkhoff and von Neumann ergodic theorems to semigroup actions, Ann. Inst. Henri Poincaré7 (1971), 283–291.

    MathSciNet  Google Scholar 

  2. L. Dubins and J. Pitman,A divergent two-parameter bounded martingale, Proc. Am. Math. Soc.78 (1980), 414–416.

    Article  MATH  MathSciNet  Google Scholar 

  3. W. Emerson,The pointwise ergodic theorem for amenable groups, Am. J. Math.96 (1974), 472–487.

    Article  MATH  MathSciNet  Google Scholar 

  4. M. Gromov,Groups of polynomial growth and expanding maps, Publ. Math. IHES53 (1981), 53–78.

    MATH  MathSciNet  Google Scholar 

  5. A. A. Tempel’man,Ergodic theorems for general dynamical systems, Dokl. Akad. Nauk SSSR176 (1967), 790–793 = Sov. Math. Dok.8 (1967), 1213–1216. Detailed proofs in: Trans. Mosc. Math. Soc.26 (1972), 94–132.

    MathSciNet  Google Scholar 

  6. G. Zbagann,On a theorem concerning covergence of martingales with N 2 as index set, Rev. Roum. Math. Pures. Appl.22 (1977), 1177–1182.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Stanford University, 94305, Stanford, CA, USA

    Donald Ornstein & Benjamin Weiss

  2. Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel

    Donald Ornstein & Benjamin Weiss

Authors
  1. Donald Ornstein
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Benjamin Weiss
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This research was supported in part by a National Science Foundation grant MCS81-07092.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ornstein, D., Weiss, B. The Shannon-McMillan-Breiman theorem for a class of amenable groups. Israel J. Math. 44, 53–60 (1983). https://doi.org/10.1007/BF02763171

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02763171

Keywords

Search

Navigation