Extensions of Borel Measurable Maps and Ranges of Borel Bimeasurable Maps

• Autorzy: Petr Holický
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
• 26A21: Classification of real functions; Baire classification of sets and functions
• 28A05: Classes of sets (Borel fields, σ -rings, etc.), measurable sets, Suslin sets, analytic sets

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2004
• Tom: 52
• Numer: 2
• Strony: 151-167

Daty

wydano

2004

Twórcy

autor

Petr Holický

• Department of Mathematical Analysis, Charles University, Sokolovská 83, 186 00 Praha 8, Czech Republic

Identyfikatory

DOI

10.4064/ba52-2-6