Radon-Nikodym theorems for set-valued measures

Fumio Hiai

Journal of Multivariate Analysis, 1978, vol. 8, issue 1, 96-118

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.

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 (search for similar items in EconPapers)
Date: 1978
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