On the absolute continuity of a class of invariant measures

DOI10.1090/S0002-9939-01-06363-8zbMath0986.28008MaRDI QIDQ2759025

Tian-You Hu, Ka-Sing Lau, Xiang-Yang Wang

Publication date: 10 December 2001

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

invariant measureiterated function systemHausdorff measureRadon-Nikodým derivativeabsolute continuityconformal IFSeigen-measures

Mathematics Subject Classification ID

Fractals (28A80) Hausdorff and packing measures (28A78)

Related Items (9)

Multifractal structure and product of matrices ⋮ On Fourier frame of absolutely continuous measures ⋮ Uniformity of measures with Fourier frames ⋮ Absolute continuity of vector-valued self-affine measures ⋮ Frame measures for infinitely many measures ⋮ On Iterated Function Systems with place-dependent probabilities ⋮ Expanding actions: minimality and ergodicity ⋮ On the absolute continuity of the Blackwell measure ⋮ Typical absolute continuity for classes of dynamically defined measures

Cites Work

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• Iterated function system and Ruelle operator
• Equivalence of positive Hausdorff measure and the open set condition for self-conformal sets
• Iterated Function Systems with Overlaps and Self-Similar Measures
• The equivalence of some Bernoulli convolutions to Lebesgue measure
• Self-similar measures and intersections of Cantor sets
• Dimensions and Measures in Infinite Iterated Function Systems
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms

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