Extensions of Borel Measurable Maps and
Ranges of Borel Bimeasurable Maps
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004) no. 2, pp. 151-167
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
We prove an abstract version of the Kuratowski extension theorem for Borel measurable maps of a given class. It enables us to deduce and improve its nonseparable version due to Hansell. We also study the ranges of not necessarily injective Borel bimeasurable maps $f$ and show that some control on the relative classes of preimages and images of Borel sets under $f$ enables one to get a bound on the absolute class of the range of $f$. This seems to be of some interest even within separable spaces.
Keywords:
prove abstract version kuratowski extension theorem borel measurable maps given class enables deduce improve its nonseparable version due hansell study ranges necessarily injective borel bimeasurable maps control relative classes preimages images borel sets under enables get bound absolute class range seems interest even within separable spaces
Affiliations des auteurs :
Petr Holický 1
@article{10_4064_ba52_2_6,
author = {Petr Holick\'y},
title = {Extensions of {Borel} {Measurable} {Maps} and
{Ranges} of {Borel} {Bimeasurable} {Maps}},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
pages = {151--167},
publisher = {mathdoc},
volume = {52},
number = {2},
year = {2004},
doi = {10.4064/ba52-2-6},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ba52-2-6/}
}
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%0 Journal Article %A Petr Holický %T Extensions of Borel Measurable Maps and Ranges of Borel Bimeasurable Maps %J Bulletin of the Polish Academy of Sciences. Mathematics %D 2004 %P 151-167 %V 52 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/ba52-2-6/ %R 10.4064/ba52-2-6 %G en %F 10_4064_ba52_2_6
Petr Holický. Extensions of Borel Measurable Maps and Ranges of Borel Bimeasurable Maps. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004) no. 2, pp. 151-167. doi: 10.4064/ba52-2-6
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