Derivability, variation and range of a vector measure
Studia Mathematica, Tome 112 (1995) no. 2, p. 165.

Voir la notice de l'article dans European Digital Mathematics Library

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.
Classification : 28B05, 46G10
Mots-clés : vector measures, range, variation, Bochner derivability, zonoid, range of a vector measure, -finiteness of its variation, derivability of the measure, Bochner derivative 
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L. Rodríguez-Piazza. Derivability, variation and range of a vector measure. Studia Mathematica, Tome 112 (1995) no. 2, p. 165. https://geodesic-test.mathdoc.fr/item/STUMA_1995__112_2_216144/