Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-26T17:56:05.511Z Has data issue: false hasContentIssue false
  • English
  • Français

On generalized Borel sets

Part of: Fairly general properties Classical measure theory

Published online by Cambridge University Press:  09 April 2009

W. F. Pfeffer
W. F. Pfeffer
Affiliation:
Department of Mathematics University of CaliforniaDavis, California 95616USA
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

Bennett, H. R. and Lutzer, D. J. (1972), “A note on weak θ-refinability”, Gen. Topology Appl. 2, 49–54.CrossRefGoogle Scholar
Dickmann, M. A. (1975), Large Infinitary Languages (North-Holland, Amsterdam).Google Scholar
Kelley, J. L. (1955), General Topology (Van Nostrand, New York).Google Scholar
Natanson, I. P. (1957), Theory of Functions of Real Variable (Ungar, New York, 1964).Google Scholar
Ulam, S. (1930), “Zur Masstheorie in der allgemeinen Mengenlehre”, Fund. Math. 16, 140–150.CrossRefGoogle Scholar