On regular generator of Z²-actions in exhaustive partitions
B. Kamiński (1987)
Studia Mathematica
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B. Kamiński (1987)
Studia Mathematica
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B. Kamiński, Z. Kowalski, P. Liardet (1997)
Studia Mathematica
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We show that for every positive integer d there exists a -action and an extremal σ-algebra of it which is not perfect.
F. Blanchard, B. Kamiński (1995)
Studia Mathematica
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We show that for every ergodic flow, given any factor σ-algebra ℱ, there exists a σ-algebra which is relatively perfect with respect to ℱ. Using this result and Ornstein's isomorphism theorem for flows, we give a functorial definition of the entropy of flows.
B. Kamiński, K. Park (1999)
Studia Mathematica
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We define the concept of directional entropy for arbitrary -actions on a Lebesgue space, we examine its basic properties and consider its behaviour in the class of product actions and rigid actions.
B. Kamiński (1990)
Studia Mathematica
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Hasfura-Buenaga, J.R. (1995)
Acta Mathematica Universitatis Comenianae. New Series
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Valentin Golodets, Sergey Sinel'shchikov (2000)
Colloquium Mathematicae
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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.
R. Burton, M. Keane, Jacek Serafin (2000)
Colloquium Mathematicae
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We present a unified approach to the finite generator theorem of Krieger, the homomorphism theorem of Sinai and the isomorphism theorem of Ornstein. We show that in a suitable space of measures those measures which define isomorphisms or respectively homomorphisms form residual subsets.
Anatole Katok, Jean-Paul Thouvenot (1997)
Annales de l'I.H.P. Probabilités et statistiques
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B. Kamiński, P. Liardet (1994)
Studia Mathematica
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Applying methods of harmonic analysis we give a simple proof of the multidimensional version of the Rokhlin-Sinaǐ theorem which states that a Kolmogorov -action on a Lebesgue space has a countable Lebesgue spectrum. At the same time we extend this theorem to -actions. Next, using its relative version, we extend to -actions some other general results connecting spectrum and entropy.