A note on Borel’s density theorem

Furstenberg, Harry

doi:10.1090/S0002-9939-1976-0422497-X

A note on Borel’s density theorem
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by Harry Furstenberg PDF

Proc. Amer. Math. Soc. 55 (1976), 209-212 Request permission

Abstract:

We prove the following theorem of Borel: If $G$ is a semisimple Lie group, $H$ a closed subgroup such that the quotient space $G/H$ carries finite measure, then for any finite-dimensional representation of $G$, each $H$-invariant subspace is $G$-invariant. The proof depends on a consideration of measures on projective spaces.

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