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New Radon–Nikodym ideals

Part of: Set theory

Published online by Cambridge University Press:  26 February 2010

Vladimir Kanovei  and
Michael Reeken
Vladimir Kanovei
Affiliation:
Moscow Center for Continuous Mathematical Education, Moscow 121002, Russia. E-mail: kanovei@math.uni-wuppertal.de
Michael Reeken
Affiliation:
Fachbereich Mathematik, Universität Wuppertal, D-42097 Wuppertal, Germany. E-mail: reeken@math.uni-wuppertal.de
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Abstract

Farah recently proved that many Borel P-ideals. on satisfy the following requirement: any measurable homomorphism has a continuous lifting which is a homomorphism itself. Ideals having such a property were called Radon–Nikodym (RN) ideals. Answering some Farah's questions, it is proved that many non-P ideals, including, for instance, Fin ⊗ Fin, are Radon–Nikodym. To prove this result, another property of ideals called the Fubini property, is introduced, which implies RN and is stable under some important transformations of ideals.

MSC classification

Secondary: 03E15: Descriptive set theory
Type
Research Article
Information
Mathematika , Volume 47 , Issue 1-2 , December 2000 , pp. 219 - 227
Copyright
Copyright © University College London 2000

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