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Proceedings of the American Mathematical Society

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A complete space of vector-valued measures


Authors: R. B. Kirk and K. Rehmer
Journal: Proc. Amer. Math. Soc. 70 (1978), 119-125
MSC: Primary 28A45
MathSciNet review: 0486401
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Abstract: Let X be a Hausdorff uniform space and E a Fréchet space (or more generally an LF-space) with dual F. Let $ {U^c}(X,E)$ denote the uniformly continuous functions from X into E which have a precompact range, and let $ {U^c}(X,E)$ have the topology of uniform convergence. Let $ L(X,F)$ be the space of all F-valued measures on X with finite support, and let $ L(X,F)$ be given the topology of uniform convergence over the uniformly equicontinuous subsets of $ {U^c}(X,E)$ having a common precompact range in E. The main result in the paper is a characterization of the completion of $ L(X,F)$ under this topology.


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DOI: https://doi.org/10.1090/S0002-9939-1978-0486401-2
Article copyright: © Copyright 1978 American Mathematical Society