A note on borel’s density theorem

Harry Furstenberg

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

A note on borel’s density theorem

Harry Furstenberg^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

52 Scopus citations

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.

Original language	English
Pages (from-to)	209-212
Number of pages	4
Journal	Proceedings of the American Mathematical Society
Volume	55
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9939-1976-0422497-X
State	Published - Feb 1976

Keywords

Lattice
Linear variety
Measure
Minimally-almost-periodic
Projective space
Representation
Semisimple group

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10.1090/S0002-9939-1976-0422497-X

Cite this

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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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AB - 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.

KW - Lattice

KW - Linear variety

KW - Measure

KW - Minimally-almost-periodic

KW - Projective space

KW - Representation

KW - Semisimple group

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A note on borel’s density theorem

Abstract

Keywords

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