A note on borel’s density theorem

Harry Furstenberg

Research output: Contribution to journalArticlepeer-review

48 Scopus citations


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 languageEnglish
Pages (from-to)209-212
Number of pages4
JournalProceedings of the American Mathematical Society
Issue number1
StatePublished - Feb 1976
Externally publishedYes


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


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