# Ergodic properties of group extensions of dynamical systems with discrete spectra

Studia Mathematica (1991)

- Volume: 101, Issue: 1, page 19-31
- ISSN: 0039-3223

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topMentzen, Mieczysław. "Ergodic properties of group extensions of dynamical systems with discrete spectra." Studia Mathematica 101.1 (1991): 19-31. <http://eudml.org/doc/215890>.

@article{Mentzen1991,

abstract = {Ergodic group extensions of a dynamical system with discrete spectrum are considered. The elements of the centralizer of such a system are described. The main result says that each invariant sub-σ-algebra is determined by a compact subgroup in the centralizer of a normal natural factor.},

author = {Mentzen, Mieczysław},

journal = {Studia Mathematica},

keywords = {ergodic group extensions; dynamical system; discrete spectrum; centralizer},

language = {eng},

number = {1},

pages = {19-31},

title = {Ergodic properties of group extensions of dynamical systems with discrete spectra},

url = {http://eudml.org/doc/215890},

volume = {101},

year = {1991},

}

TY - JOUR

AU - Mentzen, Mieczysław

TI - Ergodic properties of group extensions of dynamical systems with discrete spectra

JO - Studia Mathematica

PY - 1991

VL - 101

IS - 1

SP - 19

EP - 31

AB - Ergodic group extensions of a dynamical system with discrete spectrum are considered. The elements of the centralizer of such a system are described. The main result says that each invariant sub-σ-algebra is determined by a compact subgroup in the centralizer of a normal natural factor.

LA - eng

KW - ergodic group extensions; dynamical system; discrete spectrum; centralizer

UR - http://eudml.org/doc/215890

ER -

## References

top- [1] A. del Junco and D. Rudolph, On ergodic actions whose self-joinings are graphs, Ergodic Theory Dynamical Systems 7 (1987), 531-557. Zbl0646.60010
- [2] H. B. Keynes and D. Newton, Ergodic measures for non-abelian compact group extensions, Compositio Math. 32 (1976), 53-70. Zbl0318.28006
- [3] K. Kuratowski and C. Ryll-Nardzewski, A general theorem on selectors, Bull. Acad. Polon. Sci. 13 (1965), 397-403. Zbl0152.21403
- [4] M. Lemańczyk and M. K. Mentzen, Compact subgroups in the centralizer of natural factors determine all factors, Ergodic Theory Dynamical Systems 10 (1990), 763-776. Zbl0725.54030
- [5] D. Newton, On canonical factors of ergodic dynamical systems, J. London Math. Soc. (2) 19 (1979), 129-136. Zbl0425.28012
- [6] D. Rudolph, An example of a measure preserving map with minimal self-joinings, and applications, J. Analyse Math. 35 (1979), 97-122. Zbl0446.28018

## Citations in EuDML Documents

top- Artur Siemaszko, On group extensions of 2-fold simple ergodic actions
- A. Del Junco, M. Lemańczyk, M. Mentzen, Semisimplicity, joinings and group extensions
- M. Lemańczyk, Cohomology groups, multipliers and factors in ergodic theory
- Alexandre Danilenko, Mariusz Lemańczyk, Isometric extensions, 2-cocycles and ergodicity of skew products

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