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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Compact independent sets and Haar measures

Author: Colin C. Graham
Journal: Proc. Amer. Math. Soc. 36 (1972), 578-582
MSC: Primary 22B05; Secondary 43A05
MathSciNet review: 0313447
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Abstract: This is proved: Let H be a closed nondiscrete subgroup of an LCA group G, $ x \in G$, and $ E \subseteq G$ a $ \sigma $-compact independent subset of G; then $ H \cap (x + {G_p}E)$ has zero H-Haar measure. This generalizes a result in Rudin, Fourier analysis on groups; the proof here is quite different from that given by Rudin.

References [Enhancements On Off] (What's this?)

  • [1] Walter Rudin, Fourier analysis on groups, Interscience Tracts in Pure and Applied Mathematics, No. 12, Interscience Publishers (a division of John Wiley and Sons), New York-London, 1962. MR 0152834 (27 #2808)

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Additional Information

PII: S 0002-9939(1972)0313447-1
Keywords: Haar measure, subgroups, independent sets
Article copyright: © Copyright 1972 American Mathematical Society