Set-valued measures

Artstein, Zvi

doi:10.1090/S0002-9947-1972-0293054-4

Set-valued measures
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Trans. Amer. Math. Soc. 165 (1972), 103-125 Request permission

Abstract:

A set-valued measure is a $\sigma$-additive set-function which takes on values in the nonempty subsets of a euclidean space. It is shown that a bounded and non-atomic set-valued measure has convex values. Also the existence of selectors (vector-valued measures) is investigated. The Radon-Nikodym derivative of a set-valued measure is a set-valued function. A general theorem on the existence of R.-N. derivatives is established. The techniques require investigations of measurable set-valued functions and their support functions.

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