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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*
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 AnV, nN is said to be dominated if there exists a set BV such that AnB, for n = 1, 2, A content pC(V) is said to be Rickart on the ring V if limnp(An) = 0 for each dominated, disjoint sequence AnV, nN.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1974

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