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Hausdorff and harmonic measures on non-homogeneous Cantor sets

Abstract : We consider (not self-similar) Cantor sets defined by a sequence of piecewise linear functions. We prove that the dimension of the harmonic measure on such a set is strictly smaller than its Hausdorff dimension. Some Hausdorff measure estimates for these sets are also provided.
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https://hal.archives-ouvertes.fr/hal-00801792
Contributor : Athanasios Batakis <>
Submitted on : Monday, March 18, 2013 - 1:44:48 PM
Last modification on : Monday, June 8, 2020 - 10:38:02 AM
Document(s) archivé(s) le : Thursday, June 20, 2013 - 4:04:12 PM

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  • HAL Id : hal-00801792, version 1
  • ARXIV : 1303.4373

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Athanasios Batakis, Anna Zdunik. Hausdorff and harmonic measures on non-homogeneous Cantor sets. Annales Academiae Scientiarum Fennicae. Mathematica, Academia Scientiarum Fennica, 2015, pp.40. ⟨hal-00801792⟩

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