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Invariant measures on double coset spaces

Published online by Cambridge University Press:  09 April 2009

Teng-Sun Liu
Affiliation:
University of Pennsylvania and University of Massachusetts
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Let G be a locally compact group with left invariant Haar measure m. Le H be a closed subgroup of G and K a compact group of G. Let R be the equivalence relation in G defined by (a, b)∈R if and if a = kbh for some k in K and h in H. We call E =G/R the double coset space of G modulo K and H. Donote by a the canonical mapping of G onto E. It can be shown that E is a locally compact space and α is continous and open Let N be the normalizer of K in G, i. e. .

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1965

References

[1]Bourbaki, N., Eléments de Matématique Intégration Chaps. I–IV, Hermann Paris (19521957).Google Scholar
[2]Hewitt, E. and Ross, K. A., Abstract harmonic analysis Part I, Springer, Berlin (1963).Google Scholar
[3]Tulcea, C. Ionescu, and Simon, A. B., Spectral representations and unbounded convolution operators, Proc. Nat. Acad. Sci. U.S.A., 45 (1959) 1765–67.Google Scholar
[4]Tulcea, C. Ionescu, Generalized convolution algebras (unpublished manuscript).Google Scholar
[5]Weil, A., L'intégration dans les groupes topologiques et ses applications, Paris, 1938.Google Scholar