Positive vector measures with given marginals

Surjit Singh Khurana

Czechoslovak Mathematical Journal (2006)

  • Volume: 56, Issue: 2, page 613-619
  • ISSN: 0011-4642

Abstract

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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 × X 2 , E ) . For i = 1 , 2 , let μ i ∈ 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 .

How to cite

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Khurana, Surjit Singh. "Positive vector measures with given marginals." Czechoslovak Mathematical Journal 56.2 (2006): 613-619. <http://eudml.org/doc/31053>.

@article{Khurana2006,
abstract = {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\}$.},
author = {Khurana, Surjit Singh},
journal = {Czechoslovak Mathematical Journal},
keywords = {ordered locally convex space; order convergence; marginals; ordered locally convex space; order convergence; marginals},
language = {eng},
number = {2},
pages = {613-619},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Positive vector measures with given marginals},
url = {http://eudml.org/doc/31053},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Khurana, Surjit Singh
TI - Positive vector measures with given marginals
JO - Czechoslovak Mathematical Journal
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 2
SP - 613
EP - 619
AB - 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}$.
LA - eng
KW - ordered locally convex space; order convergence; marginals; ordered locally convex space; order convergence; marginals
UR - http://eudml.org/doc/31053
ER -

References

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  11. 10.2140/pjm.1970.33.157, Pac. J. Math. 33 (1970), 157–165. (1970) Zbl0195.14303MR0259064DOI10.2140/pjm.1970.33.157
  12. Banach Lattices, Springer-Verlag, 1991. (1991) MR1128093
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  14. 10.1214/aoms/1177700153, Ann. Math. Statist. 36 (1965), 423–439. (1965) Zbl0135.18701MR0177430DOI10.1214/aoms/1177700153
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