Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On entropy and generators of measure-preserving transformations


Author: Wolfgang Krieger
Journal: Trans. Amer. Math. Soc. 149 (1970), 453-464
MSC: Primary 28.70
Erratum: Trans. Amer. Math. Soc. 168 (1972), 519.
MathSciNet review: 0259068
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let T be an ergodic measure-preserving transformation of a Lebesgue measure space with entropy $ h(T)$. We prove that T has a generator of size k where $ {e^{h(T)}} \leqq k \leqq {e^{h(T)}} + 1$.


References [Enhancements On Off] (What's this?)

  • [1] Patrick Billingsley, Ergodic theory and information, John Wiley & Sons, Inc., New York-London-Sydney, 1965. MR 0192027
  • [2] N. Bourbaki, Éléments de mathématique. I: Les structures fondamentales de l’analyse. Fascicule VIII. Livre III: Topologie générale. Chapitre 9: Utilisation des nombres réels en topologie générale, Deuxième édition revue et augmentée. Actualités Scientifiques et Industrielles, No. 1045, Hermann, Paris, 1958 (French). MR 0173226
  • [3] Frank Hahn and William Parry, Some characteristic properties of dynamical systems with quasi-discrete spectra, Math. Systems Theory 2 (1968), 179–190. MR 0230877
  • [4] K. Jacobs, Lecture notes on ergodic theory, Aarhus Universitet, 1962/63.
  • [5] William Parry, Entropy and generators in ergodic theory, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0262464
  • [6] V. A. Rohlin, Lectures on the entropy theory of transformations with invariant measure, Uspehi Mat. Nauk 22 (1967), no. 5 (137), 3–56 (Russian). MR 0217258
  • [7] A. H. Zaslavskiĭ, On the isomorphism problem for stationary processes, Teor. Verojatnost. i Primenen. 9 (1964), 318–326 (Russian, with English summary). MR 0164377

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 28.70

Retrieve articles in all journals with MSC: 28.70


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1970-0259068-3
Keywords: Ergodic measure-preserving transformations, entropy, generators of ergodic measure-preserving transformations, shift-invariant measures, coding
Article copyright: © Copyright 1970 American Mathematical Society