Set-valued measures
Author:
Zvi Artstein
Journal:
Trans. Amer. Math. Soc. 165 (1972), 103-125
MSC:
Primary 28A45
DOI:
https://doi.org/10.1090/S0002-9947-1972-0293054-4
MathSciNet review:
0293054
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Abstract: A set-valued measure is a -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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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1972-0293054-4
Keywords:
Set-valued measure,
measurable set-valued function,
support function,
integral of a set-valued function,
selectors,
Lyapunov's convexity theorem,
Radon-Nikodym derivatives
Article copyright:
© Copyright 1972
American Mathematical Society