Hausdorff and harmonic measures on non-homogeneous Cantor sets | Zendy

Athanasios Batakis | Zendy; Anna Zdunik | Zendy

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Hausdorff and harmonic measures on non-homogeneous Cantor sets

Author(s) -

Athanasios Batakis,

Anna Zdunik

Publication year - 2015

Publication title -

annales academiae scientiarum fennicae mathematica

Language(s) - English

Resource type - Journals

eISSN - 1798-2383

pISSN - 1239-629X

DOI - 10.5186/aasfm.2015.4012

Subject(s) - hausdorff measure , hausdorff dimension , mathematics , cantor function , cantor set , outer measure , effective dimension , measure (data warehouse) , minkowski–bouligand dimension , packing dimension , piecewise linear function , dimension function , harmonic measure , homogeneous , dimension (graph theory) , harmonic , urysohn and completely hausdorff spaces , hausdorff space , cantor's diagonal argument , pure mathematics , harmonic function , mathematical analysis , fractal dimension , fractal , combinatorics , computer science , physics , database , quantum mechanics

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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