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Note on the Borel Method of Measure Extension

Published online by Cambridge University Press:  20 November 2018

G. Fox
G. Fox*
Affiliation:
Université de Montréal
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This note concerns a countably additive measure on a Boolean ring of subsets of an abstract set, this measure being real-valued, admitting ∞ as a possible value. We are interested only in unique extensions, so we suppose the measure to be σ- finite. The following well known result will be referred to as the "extension theorem": "Every σ-finite measure on a ring extends uniquely to a σ-finite measure on the generated σ-ring. "Besides the familiar proof using outer measure, there is a Borel-type proof using transfinite induction [4]. We attempt here to reduce the Borel-type proof to its ultimate simplicity, reducing the problem to the bounded case.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 5 , Issue 3 , September 1962 , pp. 285 - 296
Copyright
Copyright © Canadian Mathematical Society 1962

References

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3. Halmos, P. R., Measure Theory (New York, 1950).Google Scholar
4. LeBlanc, L. et Fox, G.E., On the Extension of Measure by the Method of Borel. Can. Jour, of Math. vol. 8, pp. 516-523, 1956.Google Scholar
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