Athanasios Batakis (2006)
Annales de l’institut Fourier
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We prove that the dimension of the harmonic measure of the complementary of a translation-invariant type of Cantor sets is a continuous function of the parameters determining these sets. This results extends a previous one of the author and do not use ergotic theoretic tools, not applicables to our case.
M. Essen, D. F. Shea, C. S. Stanton (1985)
Annales de l'institut Fourier
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We give a necessary and sufficient condition for an analytic function in to have real part in class . This condition contains the classical one of Zygmund; other variants are also given.
R. Coutinho, R. Lima, R. Vilela Mendes, S. Vaïenti (1992)
Annales de l'I.H.P. Physique théorique
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Kaufman, Robert, Llorente, José G., Wu, Jang-Mei (2003)
Annales Academiae Scientiarum Fennicae. Mathematica
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Pertti Mattila, Manuel Morán, José-Manuel Rey (2000)
Studia Mathematica
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We propose a framework to define dimensions of Borel measures in a metric space by formulating a set of natural properties for a measure-dimension mapping, namely monotonicity, bi-Lipschitz invariance, (σ-)stability, etc. We study the behaviour of most popular definitions of measure dimensions in regard to our list, with special attention to the standard correlation dimensions and their modified versions.
Magnus Carlehed (1999)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Feliks Przytycki, Mariusz Urbański, Anna Zdunik (1990)
Studia Mathematica
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