Opérations de Hausdorff itérées et réunions croissantes de compacts

• Autorzy: Sylvain Kahane
• Języki publikacji: FR

Abstrakty

EN

In this paper, motivated by questions in Harmonic Analysis, we study the operation of (countable) increasing union, and show it is not idempotent: $ω_1$ iterations are needed in general to obtain the closure of a class under this operation. Increasing union is a particular Hausdorff operation, and we present the combinatorial tools which allow to study the power of various Hausdorff operations, and of their iterates. Besides countable increasing union, we study in detail a related Hausdorff operation, which preserves compactness.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1992
• Tom: 141
• Numer: 2
• Strony: 169-194

Daty

wydano

1992

otrzymano

1991-09-09

poprawiono

1992-03-10

Twórcy

autor

Sylvain Kahane

• Equipe d'Analyse, Université Paris 6, 4, Place Jussieu, 75252 Paris Cedex 05, France

Bibliografia

• [1] B. Aniszczyk, J. Burzyk and A. Kamiński, Borel and monotone hierarchies and extension of Rényi probability spaces, Colloq. Math. 51 (1987), 11-25.
• [2] J. Arbault, Sur l'ensemble de convergence absolue d'une série trigonométrique, Bull. Soc. Math. France 80 (1952), 253-317.
• [3] H. Becker, S. Kahane and A. Louveau, Natural complete $Σ_2^1$-sets in Harmonic Analysis, Trans. Amer. Math. Soc., to appear.
• [4] G. Choquet, Sur les notions de filtre et de grille, C. R. Acad. Sci. Paris 224 (1947), 171-173.
• [5] S. Kahane, Ensembles de convergence absolue, ensembles de Dirichlet faibles et ↑-idéaux, ibid. 310 (1990), 335-337.
• [6] S. Kahane, ↑-idéaux de compacts et applications à l'analyse harmonique, Thèse, Univ. Paris 6, 1990.
• [7] S. Kahane, Antistable classes of thin sets in Harmonic Analysis, Illinois J. Math., to appear.
• [8] A. S. Kechris, A. Louveau and W. H. Woodin, The structure of σ-ideals of compact sets,Trans. Amer. Math. Soc. 301 (1987), 263-288.
• [9] K. Kuratows, Topology I, Acad. Press, New York 1966.
• [10] H. Lebesgue, Sur les fonctions représentables analytiquement, J. Math. Pures Appl. (6) 1 (1905), 139-216.