Publication date:
1 October 2017
Source:Advances in Mathematics, Volume 318
Author(s): Balázs Bárány, Antti Käenmäki
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.