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Haar Measure

  • Daniel Bump
Chapter
Part of the Graduate Texts in Mathematics book series (GTM, volume 225)

Abstract

If G is a locally compact group, there is, up to a constant multiple, a unique regular Borel measure μ L that is invariant under left translation. Here left translation invariance means that μ(X) = μ(gX) for all measurable sets X.

References

  1. 61.
    P. Halmos. Measure Theory. D. Van Nostrand Company, Inc., New York, N. Y., 1950.Google Scholar
  2. 69.
    E. Hewitt and K. Ross. Abstract Harmonic Analysis. Vol. I, Structure of topological groups, integration theory, group representations, volume 115 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, Berlin, second edition, 1979.Google Scholar
  3. 121.
    L. Loomis. An Introduction to Abstract Harmonic Analysis. D. Van Nostrand Company, Inc., Toronto-New York-London, 1953.Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Daniel Bump
    • 1
  1. 1.Department of MathematicsStanford UniversityStanfordUSA

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