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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.
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 -