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Transactions of the American Mathematical Society

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Ensembles de Riesz


Author: Valérie Tardivel
Journal: Trans. Amer. Math. Soc. 305 (1988), 167-174
MSC: Primary 43A46; Secondary 04A15
DOI: https://doi.org/10.1090/S0002-9947-1988-0920152-3
MathSciNet review: 920152
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ G$ be an abelian countable discrete group. We show that there exists no positive characterization of Riesz subsets of $ G$, by proving that the Riesz subsets of $ G$ form a coanalytic non-Borel subset of $ {2^G}$.


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

  • [D] C. Dellacherie, Ensembles analytiques: théorèmes de séparation et applications, Séminaire de Probabilités IX, Lecture Notes in Math., vol. 465, Springer-Verlag, Berlin and New York, 1975, pp. 336-372. MR 0428306 (55:1331)
  • [G-McG] C. G. Graham and O. C. McGehee, Essays in commutative harmonic analysis, Springer-Verlag, New York and Berlin, 1979. MR 550606 (81d:43001)
  • [M] Y. Meyer, Spectres des mesures et mesures absolument continues, Studia Math. 30 (1968), 87-99. MR 0227697 (37:3281)
  • [Rl] W. Rudin, Fourier analysis on groups, Interscience Tracts, no. 12, Wiley, New York, 1962. MR 0152834 (27:2808)
  • [R2] -, Real and complex analysis, 2nd ed., McGraw-Hill, New York, 1974. MR 0344043 (49:8783)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1988-0920152-3
Keywords: Riesz sets, coanalytic sets, harmonic analysis on compact abelian groups
Article copyright: © Copyright 1988 American Mathematical Society

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