Uniform absolute continuity in spaces of set functions
Author: James D. Stein
Journal: Proc. Amer. Math. Soc. 51 (1975), 137-140
MSC: Primary 28A32
MathSciNet review: 0440012
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Abstract: Let be a regular topological space, a collection of bounded regular measures defined on the Borel sets of . The following conditions are equivalent.
(1) Let denote the Borel measures, the nonnegative members of . There is a such that is uniformly -continuous.
(2) If is a disjoint sequence of open sets, then uniformly for .
(3) If is a Borel subset of and , there is a compact set such that for .
(4) If is a disjoint sequence of Borel sets, then uniformly for .
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