For stationary measures on the flags of R^d, the conditional measures along each one-dimensional flag foliation are exact dimensional with dimension equal to an entropy divided by the Lyapunov gap.
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Entropy and dimension of disintegrations of stationary measures
For stationary measures on the flags of R^d, the conditional measures along each one-dimensional flag foliation are exact dimensional with dimension equal to an entropy divided by the Lyapunov gap.