Bárány, Balázs and Käenmäki, Antti (2017) Ledrappier–Young formula and exact dimensionality of self-affine measures. ADVANCES IN MATHEMATICS, 318. ISSN 0001-8708
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Official URL: https://www.sciencedirect.com/science/article/pii/...
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.
| Item Type: | Article |
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| Subjects: | Q Science / természettudomány > QA Mathematics / matematika Q Science / természettudomány > QA Mathematics / matematika > QA74 Analysis / analízis |
| Depositing User: | Dr. Balázs Bárány |
| Date Deposited: | 19 Sep 2018 18:48 |
| Last Modified: | 05 Apr 2023 07:41 |
| URI: | http://real.mtak.hu/id/eprint/84539 |
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