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

Balázs Bárány, Antti Käenmäki

Published 2015-11-18Version 1

In this paper, we solve the long standing open problem on exact dimensionality of self-affine measures. 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 quasi self-affine measures are exact dimensional. In both cases, the measures satisfy the Ledrappier-Young formula.