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Note on Continuous and Purely Finitely Additive Set Functions

Published online by Cambridge University Press:  20 November 2018

Wilfried Siebe
Wilfried Siebe*
Affiliation:
University of Bonn Department of Economics Adenauer Allee 24-42 D - 5300 Bonn 1 Federal Republic Of Germany
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Abstract

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The Sobczyk-Hammer respectively Yosida-Hewitt decomposition ([17], [19]) generates the class of continuous respectively purely finitely additive charges. In this paper, attention is limited to hereditable properties for these classes. It is proved that the property of continuity is preserved with respect to extensions and that if all extensions of a charge to a charge on a given field are continuous, then the original charge is continuous. An analogous heredity theorem for purely finite additivity holds true in the monogenic case.

Keywords

28A10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 29 , Issue 4 , 01 December 1986 , pp. 407 - 412
Copyright
Copyright © Canadian Mathematical Society 1986

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