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On generalized Borel sets

Part of: Classical measure theory Fairly general properties

Published online by Cambridge University Press:  09 April 2009

W. F. Pfeffer
W. F. Pfeffer
Affiliation:
Department of Mathematics University of CaliforniaDavis, California 95616USA
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Abstract

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A certain natural extension B of the Borel σ-algebra is studied in generalized weakly θ-refinable spaces. It is shown that a set belongs to B whenever it belongs to B locally. From this it is derived that if ℵωα is more complicated than aunion of less than ℵα weakly θ-refinable subspaces.

Keywords

Borel setsmeasurable cardinalweakly θ-refinableregular ordinal

MSC classification

Secondary: 28A05: Classes of sets (Borel fields, $sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets 54D20: Noncompact covering properties (paracompact, Lindelöf, etc.) 28A10: Real- or complex-valued set functions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 25 , Issue 1 , February 1978 , pp. 29 - 34
Copyright
Copyright © Australian Mathematical Society 1978

References

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