Ensembles de Riesz
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- by Valérie Tardivel PDF
- Trans. Amer. Math. Soc. 305 (1988), 167-174 Request permission
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
- C. Dellacherie, Ensembles analytiques. Théorèmes de séparation et applications, Séminaire de Probabilités, IX (Seconde Partie, Univ. Strasbourg, Strasbourg, années universitaires 1973/1974 et 1974/1975), Lecture Notes in Math., Vol. 465, Springer, Berlin, 1975, pp. 336–372. MR 0428306
- Colin C. Graham and O. Carruth McGehee, Essays in commutative harmonic analysis, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 238, Springer-Verlag, New York-Berlin, 1979. MR 550606
- Yves Meyer, Spectres des mesures et mesures absolument continues, Studia Math. 30 (1968), 87–99 (French). MR 227697, DOI 10.4064/sm-30-1-87-99
- 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
- Walter Rudin, Real and complex analysis, 2nd ed., McGraw-Hill Series in Higher Mathematics, McGraw-Hill Book Co., New York-Düsseldorf-Johannesburg, 1974. MR 0344043
Additional Information
- © Copyright 1988 American Mathematical Society
- 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