Abstract
In this short note we show that any smooth probability measure on the boundaryB(G) of a semisimple Lie groupG is stationary for some probability measure on a lattice Γ. This generalizes a result of Furstenberg about Poisson boundaries for semisimple Lie groups.
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The author is supported in part by NSF postdoctoral fellowship.
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Muchnik, R. A note on stationarity of spherical measures. Isr. J. Math. 152, 271–283 (2006). https://doi.org/10.1007/BF02771987
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DOI: https://doi.org/10.1007/BF02771987