Existence and integral representation of regular extensions of measures

Werner Rinkewitz. "Existence and integral representation of regular extensions of measures." Colloquium Mathematicae 87.2 (2001): 235-243. <http://eudml.org/doc/283725>.

@article{WernerRinkewitz2001,
abstract = {Let ℒ be a δ-lattice in a set X, and let ν be a measure on a sub-σ-algebra of σ(ℒ). It is shown that ν extends to an ℒ-regular measure on σ(ℒ) provided ν*|ℒ is σ-smooth at ∅ and ν*(L) = inf ν*(U)|X ∖ U ∈ ℒ, Usupset L for all L ∈ ℒ. Moreover, a Choquet type representation theorem is proved for the set of all such extensions.},
author = {Werner Rinkewitz},
journal = {Colloquium Mathematicae},
keywords = {content; measure; regular extension; extremal; integral representation; Choquet theory},
language = {eng},
number = {2},
pages = {235-243},
title = {Existence and integral representation of regular extensions of measures},
url = {http://eudml.org/doc/283725},
volume = {87},
year = {2001},
}

TY - JOUR
AU - Werner Rinkewitz
TI - Existence and integral representation of regular extensions of measures
JO - Colloquium Mathematicae
PY - 2001
VL - 87
IS - 2
SP - 235
EP - 243
AB - Let ℒ be a δ-lattice in a set X, and let ν be a measure on a sub-σ-algebra of σ(ℒ). It is shown that ν extends to an ℒ-regular measure on σ(ℒ) provided ν*|ℒ is σ-smooth at ∅ and ν*(L) = inf ν*(U)|X ∖ U ∈ ℒ, Usupset L for all L ∈ ℒ. Moreover, a Choquet type representation theorem is proved for the set of all such extensions.
LA - eng
KW - content; measure; regular extension; extremal; integral representation; Choquet theory
UR - http://eudml.org/doc/283725
ER -