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
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