Opérations de Hausdorff itérées et réunions croissantes de compacts

Sylvain Kahane

Fundamenta Mathematicae (1992)

  • Volume: 141, Issue: 2, page 169-194
  • ISSN: 0016-2736

Abstract

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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.

How to cite

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Kahane, Sylvain. "Opérations de Hausdorff itérées et réunions croissantes de compacts." Fundamenta Mathematicae 141.2 (1992): 169-194. <http://eudml.org/doc/211959>.

@article{Kahane1992,
author = {Kahane, Sylvain},
journal = {Fundamenta Mathematicae},
keywords = {countable increasing union; Hausdorff operation; iterations; closure; compacts sets; harmonic analysis; compact thin sets; Dirichlet sets; - sets; exotic sets},
language = {fre},
number = {2},
pages = {169-194},
title = {Opérations de Hausdorff itérées et réunions croissantes de compacts},
url = {http://eudml.org/doc/211959},
volume = {141},
year = {1992},
}

TY - JOUR
AU - Kahane, Sylvain
TI - Opérations de Hausdorff itérées et réunions croissantes de compacts
JO - Fundamenta Mathematicae
PY - 1992
VL - 141
IS - 2
SP - 169
EP - 194
LA - fre
KW - countable increasing union; Hausdorff operation; iterations; closure; compacts sets; harmonic analysis; compact thin sets; Dirichlet sets; - sets; exotic sets
UR - http://eudml.org/doc/211959
ER -

References

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  6. [6] S. Kahane, ↑-idéaux de compacts et applications à l'analyse harmonique, Thèse, Univ. Paris 6, 1990. 
  7. [7] S. Kahane, Antistable classes of thin sets in Harmonic Analysis, Illinois J. Math., to appear. Zbl0793.42003
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  10. [10] H. Lebesgue, Sur les fonctions représentables analytiquement, J. Math. Pures Appl. (6) 1 (1905), 139-216. Zbl36.0453.02

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