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Regularity Properties of Measures, Entropy and the Law of the Iterated Logarithm
Author(s) -
Llorente José González,
Nicolau Artur
Publication year - 2004
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611504014844
Subject(s) - mathematics , law of the iterated logarithm , hausdorff measure , logarithm , pure mathematics , absolute continuity , entropy (arrow of time) , real line , measure (data warehouse) , euclidean space , degenerate energy levels , mathematical analysis , hausdorff dimension , physics , quantum mechanics , database , computer science
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. 2000 Mathematics Subject Classification 60G46 (primary), 28A78, 28D20 (secondary).