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Radon-Nikodym theorems for set-valued measures

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  • Hiai, Fumio

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.

Suggested Citation

  • Hiai, Fumio, 1978. "Radon-Nikodym theorems for set-valued measures," Journal of Multivariate Analysis, Elsevier, vol. 8(1), pages 96-118, March.
    • Handle: RePEc:eee:jmvana:v:8:y:1978:i:1:p:96-118
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    Cited by:

    1. D. La Torre & F. Mendivil, 2018. "Portfolio optimization under partial uncertainty and incomplete information: a probability multimeasure-based approach," Annals of Operations Research, Springer, vol. 267(1), pages 267-279, August.

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