Quotation Ararat, Çagin, Rudloff, Birgit. 2015. A Characterization Theorem for Aumann Integrals. Set-Valued Var. Anal 23 (2): S. 305-318.


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Abstract

A Daniell-Stone type characterization theorem for Aumann integrals of set-valued measurable functions will be proven. It is assumed that the values of these functions are closed convex upper sets, a structure that has been used in some recent developments in set-valued variational analysis and set optimization. It is shown that the Aumann integral of such a function is also a closed convex upper set. The main theorem characterizes the conditions under which a functional that maps from a certain collection of measurable set-valued functions into the set of all closed convex upper sets can be written as the Aumann integral with respect to some σ-finite measure. These conditions include the analog of the conlinearity and monotone convergence properties of the classical Daniell-Stone theorem for the Lebesgue integral, and three geometric properties that are peculiar to the set-valued case as they are redundant in the one-dimensional setting.

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Publication's profile

Status of publication Published
Affiliation WU
Type of publication Journal article
Journal Set-valued and Variational Analysis
Citation Index SCI
Language English
Title A Characterization Theorem for Aumann Integrals
Volume 23
Number 2
Year 2015
Page from 305
Page to 318
Reviewed? Y
URL http://arxiv.org/pdf/1404.7440.pdf
DOI http://dx.doi.org/10.1007/s11228-014-0309-0

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Rudloff, Birgit (Details)
External
Ararat, Çagin (Bilkent University, Turkey)
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