Local dimensions of measures on self-affine sets

Abstract

We show that, in a generic setting, self-affine and almost self-affine measures are exact dimensional, with local dimension equal almost everywhere to the information dimension and given by the zero of a superadditive pressure functional.

Cited by in corpus (3)

• Local Dimensions of Measures on Infinitely Generated Self-Affine Sets
• Exponential growth of norms in semigroups of linear automorphisms and Hausdorff dimension of self-projective IFS
• Multifractal formalism for almost all self-affine measures