Haar Measure

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


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.


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    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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