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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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
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