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 | References | Similar Articles | Additional Information
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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Additional Information
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