Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
Let X be a Polish space, and let $(A_p)_{p∈ω}$ be a sequence of $G_δ$ hereditary subsets of K(X) (the space of compact subsets of X). We give a general criterion which allows one to decide whether $∪_{p∈ω}A _p$ is a true $∑_3^0$ subset of K(X). We apply this criterion to show that several natural families of thin sets from harmonic analysis are true $∑_3^0$.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
181-194
Opis fizyczny
Daty
wydano
1998
otrzymano
1998-04-15
Twórcy
autor
- Université Bordeaux 1, 351, Cours de la libération, 33405 Talence Cedex, France, matheron@math.u-bordeaux.fr
Bibliografia
- [GMG] C. C. Graham and O. C. McGehee, Essays in Commutative Harmonic Analysis, Grundlehren Math. Wiss. 238, Springer, New York, 1979.
- [G] M. B. Gregory, p-Helson sets, 1 < p < 2, Israel J. Math. 12 (1972), 356-368.
- [Ke1] A. S. Kechris, Hereditary properties of the class of closed sets of uniqueness for trigonometric series, ibid. 73 (1991), 189-198.
- [Ke2] A. S. Kechris, Classical Descriptive Set Theory, Springer, New York, 1995.
- [KL] A. S. Kechris and A. Louveau, Descriptive Set Theory and the Structure of Sets of Uniqueness, London Math. Soc. Lecture Note Ser. 128, Cambridge Univ. Press, 1987.
- [LP] L.-A. Lindahl and A. Poulsen, Thin Sets in Harmonic Analysis, Marcel Dekker, New York, 1971.
- [Li] T. Linton, The H-sets of the unit circle are properly $G_{δσ}$, Real Anal. Exchange 19 (1994), 203-211.
- [Ly] R. Lyons, A new type of sets of uniqueness, Duke Math. J. 57 (1988), 431-458.
- [M] E. Matheron, The descriptive complexity of Helson sets, Illinois J. Math. 39 (1995), 608-625.
- [T] V. Tardivel, Fermés d'unicité dans les groupes abéliens localement compacts, Studia Math. 91 (1988), 1-15.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv158i2p181bwm