Geodesic
Positive vector measures with given marginals
Czechoslovak Mathematical Journal, Tome 56 (2006) no. 2, pp. 613-619
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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 $ \mu _{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 $ \mu _{1} $ and $ \mu _{2}$.
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 $ \mu _{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 $ \mu _{1} $ and $ \mu _{2}$.
Classification : 28B05, 28C05, 46E10, 46G10, 60B05
Keywords: ordered locally convex space; order convergence; marginals 
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Khurana, Surjit Singh. Positive vector measures with given marginals. Czechoslovak Mathematical Journal, Tome 56 (2006) no. 2, pp. 613-619. http://geodesic.mathdoc.fr/item/CMJ_2006_56_2_a25/

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