Geodesic
Derivability, variation and range of a vector measure
Studia Mathematica, Tome 112 (1994) no. 2, pp. 165-187

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We prove that the range of a vector measure determines the σ-finiteness of its variation and the derivability of the measure. Let F and G be two countably additive measures with values in a Banach space such that the closed convex hull of the range of F is a translate of the closed convex hull of the range of G; then F has a σ-finite variation if and only if G does, and F has a Bochner derivative with respect to its variation if and only if G does. This complements a result of [Ro] where we proved that the range of a measure determines its total variation. We also give a new proof of this fact.
DOI : 10.4064/sm-112-2-165-187
Keywords: vector measures, range, variation, Bochner derivability, zonoid

L. Rodríguez-Piazza 1

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L. Rodríguez-Piazza. Derivability, variation and range of a vector measure. Studia Mathematica, Tome 112 (1994) no. 2, pp. 165-187. doi: 10.4064/sm-112-2-165-187

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