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.
@article{bwmeta1.element.bwnjournal-article-doi-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},
volume = {52},
year = {2004},
pages = {151-167},
zbl = {1100.28004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-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) pp. 151-167. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba52-2-6/