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arXiv · 1303.4373

Hausdorff and harmonic measures on non-homogeneous Cantor sets

Athanasios Batakis·Anna Zdunik
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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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Athanasios Batakis, Anna Zdunik. 2013-03-18. Hausdorff and harmonic measures on non-homogeneous Cantor sets. https://arxiv.org/abs/1303.4373

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