Set-Valued Analysis

, Volume 2, Issue 1–2, pp 63–75 | Cite as

A unified approach to several results involving integrals of multifunctions

  • Erik J. Balder
Article
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Abstract

A well-known equivalence of randomization result of Wald and Wolfowitz states that any Young measure can be regarded as a probability measure on the set of all measurable functions. Here we give a sufficient condition for the Young measure to be equivalent to a probability measure on the set of all integrable selectors of a given multifunction. In this way, Aumann's identity for integrals of multifunctions can be interpreted in a novel fashion. By additionally applying a fundamental result from Young measure theory to uniformlyL1-bounded sequences of functions, Fatou's lemma in several dimensions, which is formulated in terms of the integral of a Kuratowski limes superior multifunction, can be proven in a new fashion. Also, a natural extension of these arguments leads to a generalization of a recent result by Artstein and Rzezuchowski [3].

Mathematics Subject Classifications (1991)

28A20 28B20 

Key words

Integrals of multifunctions Young measures equivalence of randomization 
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Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Erik J. Balder
    • 1
  1. 1.Mathematical InstituteUniversity of UtrechtUtrechtthe Netherlands

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