Borel sets with $\sigma$-compact sections for nonseparable spaces
Fundamenta Mathematicae, Tome 199 (2008) no. 2, pp. 139-154
Cet article a éte moissonné depuis 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},
year = {2008},
volume = {199},
number = {2},
doi = {10.4064/fm199-2-4},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm199-2-4/}
}
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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