Derivability, variation and range of a vector measure

• Autorzy: L. Rodríguez-Piazza
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

vector measures; range; variation; Bochner derivability; zonoid

Kategorie tematyczne

• 28B05: Vector-valued set functions, measures and integrals
• 46G10: Vector-valued measures and integration

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1994-1995
• Tom: 112
• Numer: 2
• Strony: 165-187

Daty

wydano

1995

otrzymano

1993-10-21

poprawiono

1994-02-04

Twórcy

autor

L. Rodríguez-Piazza

• Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, P.O. Box 1160, 41080 Sevilla, Spain

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