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An extension of the essential supremum concept with applications to normal integrands and multifunctions

Published online by Cambridge University Press:  17 April 2009

E.J. Balder
E.J. Balder
Affiliation:
Mathematical Institute, University of Utrecht, Budapestlaan 6, PO Box 80.010, 3508 TA Utrecht, The Netherlands.
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Abstract

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Let (T, T, μ) be a σ-finite measure space and X a Suslin space. Let A be a class of normal integrands on T × X. We discuss the existence of an essential supremum of A, namely, a normal integrand l with

where A0 is a countable subclass of A, and, for each α ∈ A,

In this way we obtain an extension of the classical essential supremum concept. The applications include a result on measurable selectors of nonmeasurable multifunctions.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 27 , Issue 3 , June 1983 , pp. 407 - 418
Copyright
Copyright © Australian Mathematical Society 1983

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