# Complete positivity of entropy and non-Bernoullicity for transformation groups

Valentin Golodets; Sergey Sinel'shchikov

Colloquium Mathematicae (2000)

- Volume: 84/85, Issue: 2, page 421-429
- ISSN: 0010-1354

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topGolodets, Valentin, and Sinel'shchikov, Sergey. "Complete positivity of entropy and non-Bernoullicity for transformation groups." Colloquium Mathematicae 84/85.2 (2000): 421-429. <http://eudml.org/doc/210823>.

@article{Golodets2000,

abstract = {The existence of non-Bernoullian actions with completely positive entropy is proved for a class of countable amenable groups which includes, in particular, a class of Abelian groups and groups with non-trivial finite subgroups. For this purpose, we apply a reverse version of the Rudolph-Weiss theorem.},

author = {Golodets, Valentin, Sinel'shchikov, Sergey},

journal = {Colloquium Mathematicae},

keywords = {complete positive entropy; Abelian group action},

language = {eng},

number = {2},

pages = {421-429},

title = {Complete positivity of entropy and non-Bernoullicity for transformation groups},

url = {http://eudml.org/doc/210823},

volume = {84/85},

year = {2000},

}

TY - JOUR

AU - Golodets, Valentin

AU - Sinel'shchikov, Sergey

TI - Complete positivity of entropy and non-Bernoullicity for transformation groups

JO - Colloquium Mathematicae

PY - 2000

VL - 84/85

IS - 2

SP - 421

EP - 429

AB - The existence of non-Bernoullian actions with completely positive entropy is proved for a class of countable amenable groups which includes, in particular, a class of Abelian groups and groups with non-trivial finite subgroups. For this purpose, we apply a reverse version of the Rudolph-Weiss theorem.

LA - eng

KW - complete positive entropy; Abelian group action

UR - http://eudml.org/doc/210823

ER -

## References

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- [2] E. Glasner, J.-P. Thouvenot and B. Weiss, Entropy theory without past, preprint ESI-612. Zbl0965.37009
- [3] V. Golodets and S. Sinel'shchikov, On the entropy theory of finitely generated nilpotent group actions, preprint.
- [4] B. Kamiński, The theory of invariant partitions for ${\mathbb{Z}}^{d}$-actions, Bull. Acad. Polon. Sci. Sér. Sci. Math. 29 (1981), 349-362. Zbl0479.28016
- [5] D. Ornstein and P. C. Shields, An uncountable family of K-automorphisms, Adv. Math. 10 (1973), 63-88. Zbl0251.28004
- [6] D. Ornstein and B. Weiss, Entropy and isomorphism theorems for actions of amenable groups, J. Anal. Math. 48 (1987), 1-141. Zbl0637.28015
- [7] V. A. Rokhlin and Ya. G. Sinai, Construction and properties of invariant meas- urable partitions, Dokl. Akad. Nauk SSSR 141 (1961), 1038-1041 (in Russian).
- [8] D. J. Rudolph and B. Weiss, Entropy and mixing for amenable group actions, preprint. Zbl0957.37003

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