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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A note on Borel's density theorem

Author: Harry Furstenberg
Journal: Proc. Amer. Math. Soc. 55 (1976), 209-212
MSC: Primary 22E40; Secondary 28A65
MathSciNet review: 0422497
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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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Keywords: Semisimple group, lattice, minimally-almost-periodic, representation, linear variety, measure, projective space
Article copyright: © Copyright 1976 American Mathematical Society

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