Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 22E40, 28A65

Retrieve articles in all journals with MSC: 22E40, 28A65


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0422497-X
PII: S 0002-9939(1976)0422497-X
Keywords: Semisimple group, lattice, minimally-almost-periodic, representation, linear variety, measure, projective space
Article copyright: © Copyright 1976 American Mathematical Society