Geodesic
Lattice-valued Borel measures. III.
Archivum mathematicum, Tome 44 (2008) no. 4, pp. 307-316.

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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.
Classification : 28A33, 28B15, 28C05, 28C15, 46B42, 46G10
Keywords: order convergence; tight and $\tau $-smooth lattice-valued vector measures; measure representation of positive linear operators; Alexandrov’s theorem 
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     author = {Khurana, Surjit Singh},
     title = {Lattice-valued {Borel} measures. {III.}},
     journal = {Archivum mathematicum},
     pages = {307--316},
     publisher = {mathdoc},
     volume = {44},
     number = {4},
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     zbl = {1212.28009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2008__44_4_a5/}
}
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Khurana, Surjit Singh. Lattice-valued Borel measures. III.. Archivum mathematicum, Tome 44 (2008) no. 4, pp. 307-316. http://geodesic.mathdoc.fr/item/ARM_2008__44_4_a5/