On classification of singular measures and fractal properties of quasi-self-affine measures in R 2

DOI10.1515/ROSE.2008.010zbMath1174.28006MaRDI QIDQ5324861

Vyacheslav Koval, Grygoriy Torbin, Mykola V. Pratsiovytyi, Sergio A. Albeverio

Publication date: 8 August 2009

Published in: Random Operators and Stochastic Equations (Search for Journal in Brave)

zbMATH Keywords

Hausdorff dimensionfractalsself-affine setssingularly continuous probability measuresDP-transformations\(Q_1^*\times Q_2^*\)-representationclassification of singular measuresQ*-representation of real numbers

Mathematics Subject Classification ID

Singular functions, Cantor functions, functions with other special properties (26A30) Metric theory of other algorithms and expansions; measure and Hausdorff dimension (11K55) Fractals (28A80) Hausdorff and packing measures (28A78)

Related Items (1)

Fractal properties of random variables with independent $Q_{\infty }$-symbols

Cites Work

• Unnamed Item
• Hausdorff dimension of the limit sets of some planar geometric constructions
• A class of self-affine sets and self-affine measures
• Fractal properties of singular probability distributions with independent \(Q^{\ast}\)-digits
• Topological and fractal properties of real numbers which are not normal
• On equivalence of infinite product measures
• The Hausdorff dimension of self-affine fractals
• On self-affine functions
• The dimension of self-affine fractals II
• The self-affine carpets of McMullen and Bedford have infinite Hausdorff measure
• Fractal probability distributions and transformations preserving the HausdorffBesicovitch dimension
• Singular Probability Distributions and Fractal Properties of Sets of Real Numbers Defined by the Asymptotic Frequencies of Their s-Adic Digits
• The Hausdorff Dimension of the Graphs of Continuous Self-Affine Functions

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