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On Uniform Semigroup-Valued Additive Set Functions

Published online by Cambridge University Press:  20 November 2018

Geoffrey Fox  and
Pedro Morales
Geoffrey Fox
Affiliation:
Département de Mathématiques et de Statistiques, Université de MontréalMontréal, Québec H3C 3J7
Pedro Morales
Affiliation:
Département de Mathématiques et D'Informatique, Université de SherbrookeSherbrooke, Québec J1K 2R1
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Abstract

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The main results of this paper are the following: (1) An extension theorem for a uniform semigroup-valued measure on a ring to the generated σ-ring. This result unifies the classieal Hahn-Carathéodory theorem, the extension theorem of Sion and a more recent result of Weber.

(2) A theorem stating that every monocompact additive uniform semigroup-valued set function on a semiring is σ-additive. This result generalizes several earlier theorems of Alexandroff, Dinculeanu-Kluvanek, Glicksberg, Huneycutt, Mallory, Marczewski, Millington and Topsøe.

Keywords

28B1004A15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 26 , Issue 1 , 01 March 1983 , pp. 26 - 34
Copyright
Copyright © Canadian Mathematical Society 1983

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