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,
${\dim }_{\mathrm{H}}\mu \circ {\pi }^{-1}=min\{1,{\dim }_{\mathrm{H}}\mu \}$
for any non-principal orthogonal projection $\pi$