# Derivability, variation and range of a vector measure

Studia Mathematica (1995)

- Volume: 112, Issue: 2, page 165-187
- ISSN: 0039-3223

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topRodríguez-Piazza, L.. "Derivability, variation and range of a vector measure." Studia Mathematica 112.2 (1995): 165-187. <http://eudml.org/doc/216144>.

@article{Rodríguez1995,

abstract = {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.},

author = {Rodríguez-Piazza, L.},

journal = {Studia Mathematica},

keywords = {vector measures; range; variation; Bochner derivability; zonoid; range of a vector measure; -finiteness of its variation; derivability of the measure; Bochner derivative},

language = {eng},

number = {2},

pages = {165-187},

title = {Derivability, variation and range of a vector measure},

url = {http://eudml.org/doc/216144},

volume = {112},

year = {1995},

}

TY - JOUR

AU - Rodríguez-Piazza, L.

TI - Derivability, variation and range of a vector measure

JO - Studia Mathematica

PY - 1995

VL - 112

IS - 2

SP - 165

EP - 187

AB - 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.

LA - eng

KW - vector measures; range; variation; Bochner derivability; zonoid; range of a vector measure; -finiteness of its variation; derivability of the measure; Bochner derivative

UR - http://eudml.org/doc/216144

ER -

## References

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