Comptes Rendus
no. 13-14
Mathematical Analysis
Baire category and zero sets
[Ensembles de zéros et catégorie de Baire]

Présenté par : Jean-Pierre Kahane

Thomas Körner1
1 DPMMS, Centre for Mathematical Sciences, Clarkson Road, Cambridge CB3 0WB, UK
Comptes Rendus. Mathématique, Volume 346 (2008) no. 13-14, pp. 741-743.

Quasi-surement, les zéros d'une fonction continue forment un ensemble de Kronecker parfait de dimension d'Haudorff zéro.

Quasi-all continuous functions have a zero set which is a perfect Kronecker set with Hausdorff dimension zero.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2008.05.005
Thomas Körner 1

1 DPMMS, Centre for Mathematical Sciences, Clarkson Road, Cambridge CB3 0WB, UK 
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Thomas Körner. Baire category and zero sets. Comptes Rendus. Mathématique, Volume 346 (2008) no. 13-14, pp. 741-743. doi : 10.1016/j.crma.2008.05.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.05.005/

[1] J.P. Kahane Some Random Series of Functions, Cambridge Studies in Advanced Mathematics, vol. 5, Cambridge University Press, Cambridge, 1985

[2] T.W. Körner, Variations on a theme of Debs and Saint Raymond, J. LMS, in press

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