Geodesic
Borel sets with $\sigma$-compact sections for nonseparable spaces
Petr Holický1
1 Department of Mathematical Analysis Faculty of Mathematics and Physics Charles University Sokolovská 83 186 75 Praha 8, Czech Republic
Fundamenta Mathematicae, Tome 199 (2008) no. 2, pp. 139-154.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We prove that every (extended) Borel subset $E$ of $X\times Y$, where $X$ is complete metric and $Y$ is Polish, can be covered by countably many extended Borel sets with compact sections if the sections $E_x=\{y\in Y:(x,y)\in E\}$, $x\in X$, are $\sigma$-compact. This is a nonseparable version of a theorem of Saint Raymond. As a by-product, we get a proof of Saint Raymond's result which does not use transfinite induction.
DOI : 10.4064/fm199-2-4
Keywords: prove every extended borel subset times where complete metric polish covered countably many extended borel sets compact sections sections sigma compact nonseparable version theorem saint raymond by product get proof saint raymonds result which does transfinite induction

Petr Holický 1

1 Department of Mathematical Analysis Faculty of Mathematics and Physics Charles University Sokolovská 83 186 75 Praha 8, Czech Republic 
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Petr Holický. Borel sets with $\sigma$-compact sections for nonseparable spaces. Fundamenta Mathematicae, Tome 199 (2008) no. 2, pp. 139-154. doi : 10.4064/fm199-2-4. http://geodesic.mathdoc.fr/articles/10.4064/fm199-2-4/

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