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Proceedings of the American Mathematical Society

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Metric invariance of Haar measure


Author: Christoph Bandt
Journal: Proc. Amer. Math. Soc. 87 (1983), 65-69
MSC: Primary 43A05; Secondary 28C10
DOI: https://doi.org/10.1090/S0002-9939-1983-0677233-2
MathSciNet review: 677233
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Abstract: Let $ d$ be a left invariant metric for a locally compact group $ G$. We prove that isometric subsets of $ (G,d)$ have equal Haar measure.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0677233-2
Keywords: Haar measure, isometric sets, Hausdorff measure, fractional covering, multiple covering
Article copyright: © Copyright 1983 American Mathematical Society