# A note on the entropy of a doubly stochastic operator

Brunon Kamiński; José de Sam Lazaro

Colloquium Mathematicae (2000)

- Volume: 84/85, Issue: 1, page 245-254
- ISSN: 0010-1354

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topKamiński, Brunon, and de Sam Lazaro, José. "A note on the entropy of a doubly stochastic operator." Colloquium Mathematicae 84/85.1 (2000): 245-254. <http://eudml.org/doc/210803>.

@article{Kamiński2000,

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.},

author = {Kamiński, Brunon, de Sam Lazaro, José},

journal = {Colloquium Mathematicae},

keywords = {measurable partitions; doubly stochastic operator; Koopman operator; entropy; conditional entropy},

language = {eng},

number = {1},

pages = {245-254},

title = {A note on the entropy of a doubly stochastic operator},

url = {http://eudml.org/doc/210803},

volume = {84/85},

year = {2000},

}

TY - JOUR

AU - Kamiński, Brunon

AU - de Sam Lazaro, José

TI - A note on the entropy of a doubly stochastic operator

JO - Colloquium Mathematicae

PY - 2000

VL - 84/85

IS - 1

SP - 245

EP - 254

AB - 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.

LA - eng

KW - measurable partitions; doubly stochastic operator; Koopman operator; entropy; conditional entropy

UR - http://eudml.org/doc/210803

ER -

## References

top- [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. Zbl0595.60004
- [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. Zbl0138.10402
- [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).

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