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Proceedings of the American Mathematical Society

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

 
 

 

Locally compact spaces of measures


Author: Norman Y. Luther
Journal: Proc. Amer. Math. Soc. 25 (1970), 541-547
MSC: Primary 28.30; Secondary 54.00
DOI: https://doi.org/10.1090/S0002-9939-1970-0280668-4
MathSciNet review: 0280668
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Abstract: Under varying conditions on the topological space $X$, the spaces of $\sigma$-smooth, $\tau$-smooth, and tight measures on $X$, respectively, are each shown to be locally compact in the weak topology if, and only if, $X$ is compact.


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Keywords: Finitely additive measures, signed measures, zero sets, co-zero sets, <IMG WIDTH="18" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$\sigma$">-smooth measures, <IMG WIDTH="17" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img2.gif" ALT="$\tau$">-smooth measures, tight measures, weak topology, locally compact spaces of measures, compact sets of measures, two-valued measures, degenerate measures, bounded continuous functions
Article copyright: © Copyright 1970 American Mathematical Society