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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm87-2-9,
author = {Werner Rinkewitz},
title = {Existence and integral representation of regular extensions of measures},
journal = {Colloquium Mathematicae},
volume = {89},
year = {2001},
pages = {235-243},
zbl = {0984.28001},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm87-2-9}
}
Werner Rinkewitz. Existence and integral representation of regular extensions of measures. Colloquium Mathematicae, Tome 89 (2001) pp. 235-243. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm87-2-9/