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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Compact independent sets and Haar measures
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by Colin C. Graham PDF
Proc. Amer. Math. Soc. 36 (1972), 578-582 Request permission

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
  • Walter Rudin, Fourier analysis on groups, Interscience Tracts in Pure and Applied Mathematics, No. 12, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0152834
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 36 (1972), 578-582
  • MSC: Primary 22B05; Secondary 43A05
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0313447-1
  • MathSciNet review: 0313447