Lattice-valued Borel measures. III.

Surjit Singh Khurana

Archivum Mathematicum (2008)

  • Volume: 044, Issue: 4, page 307-316
  • ISSN: 0044-8753

Abstract

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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 the points of E , an Alexanderov’s type theorem is proved for a sequence of σ -additive measures.

How to cite

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Khurana, Surjit Singh. "Lattice-valued Borel measures. III.." Archivum Mathematicum 044.4 (2008): 307-316. <http://eudml.org/doc/250471>.

@article{Khurana2008,
abstract = {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.},
author = {Khurana, Surjit Singh},
journal = {Archivum Mathematicum},
keywords = {order convergence; tight and $\tau $-smooth lattice-valued vector measures; measure representation of positive linear operators; Alexandrov’s theorem; order convergence; tight measure; -smooth lattice-valued vector measure; measure representation; positive linear operator; Alexandrov's theorem},
language = {eng},
number = {4},
pages = {307-316},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Lattice-valued Borel measures. III.},
url = {http://eudml.org/doc/250471},
volume = {044},
year = {2008},
}

TY - JOUR
AU - Khurana, Surjit Singh
TI - Lattice-valued Borel measures. III.
JO - Archivum Mathematicum
PY - 2008
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 044
IS - 4
SP - 307
EP - 316
AB - 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.
LA - eng
KW - order convergence; tight and $\tau $-smooth lattice-valued vector measures; measure representation of positive linear operators; Alexandrov’s theorem; order convergence; tight measure; -smooth lattice-valued vector measure; measure representation; positive linear operator; Alexandrov's theorem
UR - http://eudml.org/doc/250471
ER -

References

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