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The range of a vector measure and a Radon-Nikodým problem for the variation. (English) Zbl 0917.46043

Summary: We show that the range of a vector measure of bounded variation determines the existence of a norm one derivative of the variation with respect to the measure. We also characterize those ranges of \(L^1(\lambda)\)-valued vector measures with this property.

MSC:

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