Borel sets with $\sigma$-compact sections for nonseparable spaces
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.
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
Affiliations des auteurs :
Petr Holický 1
@article{10_4064_fm199_2_4,
author = {Petr Holick\'y},
title = {Borel sets with $\sigma$-compact sections for nonseparable spaces},
journal = {Fundamenta Mathematicae},
pages = {139--154},
publisher = {mathdoc},
volume = {199},
number = {2},
year = {2008},
doi = {10.4064/fm199-2-4},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm199-2-4/}
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TY - JOUR AU - Petr Holický TI - Borel sets with $\sigma$-compact sections for nonseparable spaces JO - Fundamenta Mathematicae PY - 2008 SP - 139 EP - 154 VL - 199 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/fm199-2-4/ DO - 10.4064/fm199-2-4 LA - en ID - 10_4064_fm199_2_4 ER -
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
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