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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Weak compactness of certain sets of measures


Author: Surjit Singh Khurana
Journal: Proc. Amer. Math. Soc. 131 (2003), 3251-3255
MSC (2000): Primary 60B10, 46G10, 46G15, 28C15; Secondary 47B38, 28A51, 54C35
Published electronically: January 8, 2003
MathSciNet review: 1992866
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Abstract: For a compact Hausdorff space $X$ and a Montel Hausdorff locally convex space $E$, let $ F= (C(X, E), u),\; u$ being the uniform topology. We determine the necessary and sufficient conditions for an equicontinuous $ H \subset F' $ to be $ \sigma(F', F'') $-compact. Special results are obtained when $X$ is an $F$-space or a $\sigma$-Stonian space.


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Additional Information

Surjit Singh Khurana
Affiliation: Department of Mathematics, University of Iowa, Iowa City, Iowa 52242
Email: skhurana@blue.weeg.uiowa.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-03-06877-1
PII: S 0002-9939(03)06877-1
Keywords: Montel locally convex space, Stonian space, Fr\'{e}chet space, lifting of measures
Received by editor(s): January 2, 2002
Received by editor(s) in revised form: April 28, 2002
Published electronically: January 8, 2003
Communicated by: Claudia M. Neuhauser
Article copyright: © Copyright 2003 American Mathematical Society