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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Furstenberg 措施的精确维度

对于SL_d({\mathbb {R}}) \ )上的概率测度\( \mu \ ) ，我们考虑标志空间上的 Furstenberg 平稳测度\( \nu \) 。在一般非退化条件下，如果\( \mu \)是离散的并且如果\( \sum _g \log \Vert g\Vert \, \mu (g) < + \infty \)，则测度\( \ nu \)是精确维度的。