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Extensions of Borel measurable maps and ranges of Borel bimeasurable maps

Holicky P.

Bulletin of the Polish Academy of Sciences. Mathematics

2004

Vol. 52, nr 2

151-167

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 bimea-surable 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.