An axiomatic definition of the entropy of a -action on a Lebesgue space
B. Kamiński (1990)
Studia Mathematica
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B. Kamiński (1990)
Studia Mathematica
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S. Thangavelu (1991)
Studia Mathematica
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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.
Zbigniew Kowalski (1988)
Studia Mathematica
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Mark Fannes (1998)
Banach Center Publications
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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.
Mariusz Lemańczyk (1985)
Studia Mathematica
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Anatole Katok, Jean-Paul Thouvenot (1997)
Annales de l'I.H.P. Probabilités et statistiques
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Wen Huang, Alejandro Maass, Xiangdong Ye (2004)
Annales de l’institut Fourier
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In this paper we explore topological factors in between the Kronecker factor and the maximal equicontinuous factor of a system. For this purpose we introduce the concept of sequence entropy -tuple for a measure and we show that the set of sequence entropy tuples for a measure is contained in the set of topological sequence entropy tuples [H- Y]. The reciprocal is not true. In addition, following topological ideas in [BHM], we introduce a weak notion and a strong notion of complexity...