Ledrappier-Young formula and exact dimensionality of self-affine measures
arXiv:1511.05792 · doi:10.1016/j.aim.2017.07.015
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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