The dimension of projections of planar diagonal self-affine measures

Abstract

We show that if \(\mu\) is a self-affine measure on the plane defined by an iterated function system of contractions with diagonal linear parts, then under an irrationality assumption on the entries of the linear parts,
\(\operatorname{dim}_{\rm H} \mu \circ \pi^{-1} = \min \{ 1, \operatorname{dim}_{\rm H} \mu \}\)
for any non-principal orthogonal projection \(\pi\).