ArticleOriginal scientific text

Title

A note on the entropy of a doubly stochastic operator

Authors 1, 2

Affiliations

  1. Faculty of Mathematics and Informatics, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland
  2. Département de Mathématiques, Université de Rouen, Site Colbert, 76130 Mont-Saint-Aignan, France

Abstract

We investigate the properties of the entropy and conditional entropy of measurable partitions of unity in the space of essentially bounded functions defined on a Lebesgue probability space.

Bibliography

  1. E. Ghys, R. Langevin et P. Walczak, Entropie mesurée et partitions de l'unité, C. R. Acad. Sci. Paris Sér. I 303 (1986), 251-254.
  2. A. Iwanik, Pointwise induced semigroups of σ-endomorphisms, Colloq. Math. 38 (1977), 27-35.
  3. P. A. Meyer, Probabilités et Potentiel, Hermann, Paris, 1966.
  4. V. A. Rokhlin, Lectures on the entropy theory of transformations with invariant measure, Uspekhi Mat. Nauk 22 (1967), no. 3, 3-56 (in Russian).
Pages:
245-254
Main language of publication
English
Received
1999-07-16
Accepted
1999-11-04
Published
2000
Exact and natural sciences