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arXiv · 1511.05792

Ledrappier-Young formula and exact dimensionality of self-affine measures

Balázs Bárány·Antti Käenmäki
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Abstract

In this paper, we solve the long standing open problem on exact dimensionality of self-affine measures on the plane. We show that every self-affine measure on the plane is exact dimensional regardless of the choice of the defining iterated function system. In higher dimensions, under certain assumptions, we prove that self-affine and quasi self-affine measures are exact dimensional. In both cases, the measures satisfy the Ledrappier-Young formula.

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Balázs Bárány, Antti Käenmäki. 2015-11-18. Ledrappier-Young formula and exact dimensionality of self-affine measures. https://doi.org/10.1016/j.aim.2017.07.015

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