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Regularity properties of measures, entropy and the Law of the Iterated Logarithm

Published online by Cambridge University Press:  08 September 2004

José González Llorente  and
Artur Nicolau
José González Llorente
Affiliation:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain. E-mail: gonzalez@mat.uab.es
Artur Nicolau
Affiliation:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain. E-mail: gonzalez@mat.uab.es
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Abstract

We study regularity properties of a positive measure in euclidean space, such as being absolutely continuous with respect to certain Hausdorff measures, in terms of their dyadic doubling properties. Applications of the main results to the distortion of homeomorphisms of the real line and to the regularity of the harmonic measure for some degenerate elliptic operators are given.

Keywords

60G46 (primary)28A7828D20 (secondary)
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 89 , Issue 2 , September 2004 , pp. 485 - 524
Copyright
2004 London Mathematical Society

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Footnotes

The authors are partially supported by DGICYT and CIRIT grants.