Radon-Nikodym theorems for set-valued measures

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Abstract

Set-valued measures whose values are subsets of a Banach space are studied. Some basic properties of these set-valued measures are given. Radon-Nikodym theorems for set-valued measures are established, which assert that under suitable assumptions a set-valued measure is equal (in closures) to the indefinite integral of a set-valued function with respect to a positive measure. Set-valued measures with compact convex values are particularly considered.

MSC

28A45
46G05
46G10
46E30

Keywords

Radon-Nikodym property
set-valued measures
countable additivity
atoms
Hausdorff metric
selections
set-valued functions
integrable boundedness
Radon-Nikodym derivatives
generalized Radon-Nikodym derivatives

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