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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Lattice-valued Borel measures. II


Author: Surjit Singh Khurana
Journal: Trans. Amer. Math. Soc. 235 (1978), 205-211
MSC: Primary 28A55
DOI: https://doi.org/10.1090/S0002-9947-1978-0460590-2
MathSciNet review: 0460590
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Abstract: Let T be a completely regular Hausdorff space, ${C_b}(T)$ the set of all bounded real-valued continuous functions on T, E a boundedly monotone complete ordered vector space, and $\varphi :{C_b}(T) \to E$ a positive linear map. It is proved that under certain conditions there exist $\sigma$-additive, $\tau$-smooth or tight E-valued measures on T which represent $\varphi$.


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Keywords: <IMG WIDTH="17" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img5.gif" ALT="$\tau$">-smooth measures, tight measures, weakly <IMG WIDTH="18" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img4.gif" ALT="$\sigma$">-distributive lattices, monotone order <IMG WIDTH="18" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img11.gif" ALT="$\sigma$">-continuous, order <IMG WIDTH="18" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$\sigma$">-continuous, monotone order <IMG WIDTH="18" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img2.gif" ALT="$\sigma$">-closed, order <IMG WIDTH="18" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img3.gif" ALT="$\sigma$">-closed
Article copyright: © Copyright 1978 American Mathematical Society