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28d20 (secondary)

Proceedings of the London Mathematical Society (1)

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Regularity properties of measures, entropy and the Law of the Iterated Logarithm
José González Llorente, Artur Nicolau
Journal:

Proceedings of the London Mathematical Society / Volume 89 / Issue 2 / September 2004

Published online by Cambridge University Press:

08 September 2004, pp. 485-524

Print publication:

September 2004
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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.