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