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

Oberle, Richard Alan

Canadian journal of mathematics, Tome 26 (1974) no. 2, pp. 281-290

Résumé

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 limn p(An ) = 0 for each dominated, disjoint sequence An ∊ V, n ∊ N.

Détail

DOI : 10.4153/CJM-1974-029-x

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