Ensembles de Riesz

Tardivel, Valérie

doi:10.1090/S0002-9947-1988-0920152-3

Ensembles de Riesz
HTML articles powered by AMS MathViewer

by Valérie Tardivel

Trans. Amer. Math. Soc. 305 (1988), 167-174

DOI: https://doi.org/10.1090/S0002-9947-1988-0920152-3

PDF | 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, Lecture Notes in Math., Vol. 465, Springer, Berlin, 1975, pp. 336–372. Seconde Partie, Univ. Strasbourg, Strasbourg, années universitaires 1973/1974 et 1974/1975,. 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