Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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
DOI: https://doi.org/10.1090/S0002-9939-1978-0486401-2
MathSciNet review: 0486401
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 28A45

Retrieve articles in all journals with MSC: 28A45


Additional Information

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

American Mathematical Society