We prove that in any compact symmetric space, G/K, there is a dense set of a1,a2G such that if j=mKajmk is the K-bi-invariant measure supported on KajK, then 12 is absolutely continuous with respect to Haar measure on G. Moreover, the product of double cosets, Ka1Ka2K, has nonempty interior in G.
- absolutely continuous measure
- compact symmetric space
- double coset
ASJC Scopus subject areas