Exact dimension of Furstenberg measures

Abstract

For a probability measure $\mu$ on SL d (R), we consider the Furstenberg stationary measure on the space of flags. Under general non-degeneracy conditions, if $\mu$ is discrete and if g log g d$\mu$(g) < +$\infty$, then the measure $\nu$ is exact-dimensional.

References in corpus (2)

• Ledrappier-Young formula and exact dimensionality of self-affine measures
• Entropies of compact strictly convex projective manifolds