Ledrappier-Young formula and exact dimensionality of self-affine measures
Bárány, B., & Käenmäki, A. (2017). Ledrappier-Young formula and exact dimensionality of self-affine measures. Advances in Mathematics, 318 (1), 88-129. doi:10.1016/j.aim.2017.07.015
Published inAdvances in Mathematics
© 2017 Elsevier Inc. This is a final draft version of an article whose final and definitive form has been published by Elsevier. Published in this repository with the kind permission of the publisher.
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.