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Characterization of a Class of Equicontinuous Sets of Finitely Additive Measures with an Application to Vector Valued Borel Measures

Published online by Cambridge University Press:  20 November 2018

Richard Alan Oberle
Richard Alan Oberle*
Affiliation:
The Center for Naval Analyses, Arlington, Virginia
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Let V denote a ring of subsets of an abstract space X, let R+ denote the nonnegative reals, and let N denote the set of positive integers. We denote by C(V) the space of all subadditive and increasing functions, from the ring V into R+, which are zero at the empty set. The space C(V) is called the space of contents on the ring V and elements are referred to as contents.

A sequence of sets An ∊ V, n ∊ N is said to be dominated if there exists a set B ∊ V such that An ⊆ B, for n = 1, 2, A content p ∊ C(V) is said to be Rickart on the ring V if limnp(An) = 0 for each dominated, disjoint sequence An ∊ V, n ∊ N.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 2 , April 1974 , pp. 281 - 290
Copyright
Copyright © Canadian Mathematical Society 1974

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