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The balls do not generate all Borel sets using complements and countable disjoint unions

Published online by Cambridge University Press:  01 May 2000

T. KELETI  and
D. PREISS
T. KELETI
Affiliation:
Department of Analysis, Eötvös Loránd University, Múzeum krt. 6–8, 1088 Budapest, Hungary. e-mail: elek@cs.elte.hu
D. PREISS
Affiliation:
Department of Mathematics, University College London, Gower Street, London WC1E 6BT. e-mail: dp@math.ucl.ac.uk
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Abstract

We prove that in a separable infinite dimensional Hilbert space the Dynkin system generated by the family of all open balls (that is, the smallest collection containing the open balls and closed under complements and countable disjoint unions) does not contain all Borel sets.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 128 , Issue 3 , May 2000 , pp. 539 - 547
Copyright
The Cambridge Philosophical Society 2000

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