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On entropy and Hausdorff dimension of measures defined through a non-homogeneous Markov process

Athanasios Batakis (2006)

Colloquium Mathematicae

We study the Hausdorff dimension of measures whose weight distribution satisfies a Markov non-homogeneous property. We prove, in particular, that the Hausdorff dimensions of this kind of measures coincide with their lower Rényi dimensions (entropy). Moreover, we show that the packing dimensions equal the upper Rényi dimensions. As an application we get a continuity property of the Hausdorff dimension of the measures, when viewed as a function of the distributed weights under the $ℓ^{\infty}$ norm.

On Ergodic Averages for Affine Lattice Actions on Tori.

S.G. Dani, S. Muralidharan (1983)

Monatshefte für Mathematik

On Ergodic Flows and the Isomorphism of Factors.

Wolfgang Krieger (1976)

Mathematische Annalen

On Ergodic Properties of Inner Functions.

Ch. Pommerenke (1981)

Mathematische Annalen

On ergodic singular integral operators

A. Alphonse, Shobha Madan (1993)

Colloquium Mathematicae

On Ergodic Theory of A. Schmidt's Complex Continued Fractions over Gaussian Field.

Hitoshi Nakada (1988)

Monatshefte für Mathematik

On essential cluster sets

S. Mukhopadhyay (1973)

Fundamenta Mathematicae

On Exact Toral Endomorphisms.

Karol Krzyzewski (1993)

Monatshefte für Mathematik

On extension of Baire submeasures

Ivan Dobrakov (1985)

Mathematica Slovaca

On extension of Baire vector measures

Miloslav Duchoň (1986)

Mathematica Slovaca

On extension of group valued measures

Ján Šipoš (1990)

Mathematica Slovaca

On extension of maps with values in ordered spaces

Peter Volauf (1980)

Mathematica Slovaca

On extension of submeasures

Ivan Dobrakov (1984)

Mathematica Slovaca

On extension of vector polymeasures

Ivan Dobrakov (1988)

Czechoslovak Mathematical Journal

On extension of vector polymeasures. II.

Ivan Dobrakov (1995)

Mathematica Slovaca

On extensions of measures

K. P. S. Bhaskara Rao, B. V. Rao (1987)

Colloquium Mathematicae

On extensions of $σ$ -fields of sets

Edward Grzegorek (1993)

Acta Universitatis Carolinae. Mathematica et Physica

On extremal and perfect σ-algebras for $ℤ^{d}$ -actions on a Lebesgue space

B. Kamiński, Z. Kowalski, P. Liardet (1997)

Studia Mathematica

We show that for every positive integer d there exists a $ℤ^{d}$ -action and an extremal σ-algebra of it which is not perfect.

On extremal and perfect σ-algebras for flows

B. Kamiński, Z. Kowalski (1998)

Studia Mathematica

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.

On fields and ideals connected with notions of forcing

W. Kułaga (2006)

Colloquium Mathematicae

We investigate an algebraic notion of decidability which allows a uniform investigation of a large class of notions of forcing. Among other things, we show how to build σ-fields of sets connected with Laver and Miller notions of forcing and we show that these σ-fields are closed under the Suslin operation.

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