An axiomatic definition of the entropy of a -action on a Lebesgue space
B. Kamiński (1990)
Studia Mathematica
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Displaying similar documents to “On regular generator of Z²-actions in exhaustive partitions”
An axiomatic definition of the entropy of a -action on a Lebesgue space
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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.
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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...