Extensions of Borel Measurable Maps and Ranges of Borel Bimeasurable Maps

Petr Holický. "Extensions of Borel Measurable Maps and Ranges of Borel Bimeasurable Maps." Bulletin of the Polish Academy of Sciences. Mathematics 52.2 (2004): 151-167. <http://eudml.org/doc/280448>.

@article{PetrHolický2004,
abstract = {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.},
author = {Petr Holický},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {absolute Borel sets; Borel classes; Borel isomorphisms; nonseparable spaces; scattered families},
language = {eng},
number = {2},
pages = {151-167},
title = {Extensions of Borel Measurable Maps and Ranges of Borel Bimeasurable Maps},
url = {http://eudml.org/doc/280448},
volume = {52},
year = {2004},
}

TY - JOUR
AU - Petr Holický
TI - Extensions of Borel Measurable Maps and Ranges of Borel Bimeasurable Maps
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2004
VL - 52
IS - 2
SP - 151
EP - 167
AB - 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.
LA - eng
KW - absolute Borel sets; Borel classes; Borel isomorphisms; nonseparable spaces; scattered families
UR - http://eudml.org/doc/280448
ER -