Displaying similar documents to “On extremal and perfect σ-algebras for ℤ d -actions on a Lebesgue space”

On extremal and perfect σ-algebras for flows

B. Kamiński, Z. Kowalski (1998)

Studia Mathematica

Similarity:

It is shown that there exists a flow on a Lebesgue space with finite entropy and an extremal σ-algebra of it which is not perfect.

Sequence entropy pairs and complexity pairs for a measure

Wen Huang, Alejandro Maass, Xiangdong Ye (2004)

Annales de l’institut Fourier

Similarity:

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 n -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...

Relatively perfect σ-algebras for flows

F. Blanchard, B. Kamiński (1995)

Studia Mathematica

Similarity:

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.

On the directional entropy for ℤ²-actions on a Lebesgue space

B. Kamiński, K. Park (1999)

Studia Mathematica

Similarity:

We define the concept of directional entropy for arbitrary ℤ 2 -actions on a Lebesgue space, we examine its basic properties and consider its behaviour in the class of product actions and rigid actions.

Sequence entropy and rigid σ-algebras

Alvaro Coronel, Alejandro Maass, Song Shao (2009)

Studia Mathematica

Similarity:

We study relationships between sequence entropy and the Kronecker and rigid algebras. Let (Y,,ν,T) be a factor of a measure-theoretical dynamical system (X,,μ,T) and S be a sequence of positive integers with positive upper density. We prove there exists a subsequence A ⊆ S such that h μ A ( T , ξ | ) = H μ ( ξ | ( X | Y ) ) for all finite partitions ξ, where (X|Y) is the Kronecker algebra over . A similar result holds for rigid algebras over . As an application, we characterize compact, rigid and mixing extensions via relative...