Let $X$ be a completely regular $T_{1}$ space, $E$ a boundedly complete vector lattice, $ C(X)$ $(C_{b}(X))$ the space of all (all, bounded), real-valued continuous functions on $X$. In order convergence, we consider $E$-valued, order-bounded, $\sigma $-additive, $\tau $-additive, and tight measures on X and prove some order-theoretic and topological properties of these measures. Also for an order-bounded, $E$-valued (for some special $E$) linear map on $C(X)$, a measure representation result is proved. In case $E_{n}^{*}$ separates the points of $E$, an Alexanderov’s type theorem is proved for a sequence of $\sigma $-additive measures.
@article{119770,
author = {Surjit Singh Khurana},
title = {Lattice-valued Borel measures. III.},
journal = {Archivum Mathematicum},
volume = {044},
year = {2008},
pages = {307-316},
zbl = {1212.28009},
mrnumber = {2493427},
language = {en},
url = {http://dml.mathdoc.fr/item/119770}
}
Khurana, Surjit Singh. Lattice-valued Borel measures. III.. Archivum Mathematicum, Tome 044 (2008) pp. 307-316. http://gdmltest.u-ga.fr/item/119770/
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