Order convergence of vector measures on topological spaces

Surjit Singh Khurana

Positive vector measures with given marginals

Surjit Singh Khurana (2006)

Czechoslovak Mathematical Journal

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Suppose $E$ is an ordered locally convex space, $X_{1}$ and $X_{2}$ Hausdorff completely regular spaces and $Q$ a uniformly bounded, convex and closed subset of $M_{t}^{+} (X_{1} \times X_{2}, E)$ . For $i = 1, 2$ , let $μ_{i} \in M_{t}^{+} (X_{i}, E)$ . Then, under some topological and order conditions on $E$ , necessary and sufficient conditions are established for the existence of an element in $Q$ , having marginals $μ_{1}$ and $μ_{2}$ .

Lattice-valued Borel measures. III.

Surjit Singh Khurana (2008)

Archivum Mathematicum

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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, $σ$ -additive, $τ$ -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...

Displaying similar documents to “Order convergence of vector measures on topological spaces”

Positive vector measures with given marginals

Lattice-valued Borel measures. III.