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

José González Llorente, Artur Nicolau Nos

• 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.