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Multifunctions of Souslin type

Published online by Cambridge University Press:  17 April 2009

S.J. Leese
S.J. Leese
Affiliation:
Department of Mathematics, University of Western Australia, Nedlands, Western Australia.
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Abstract

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Let S and X be any two sets; then a mapping Γ which assigns to each point t in S a set Γ(t) of points in X is called a multifunction from S into X. A selector for Γ is a function f from S into X such that f(t) ∈ Γ(t) for each t. We introduce here a class of multifunctions which is both well-supplied with measurable selectors and yet is comprehensive enough to include those kinds of multifunction which have been most commonly studied before. Hence in order to show that a multifunction with non-empty values, which may arise naturally in an implicit function problem, has a measurable selector, it is sufficient to show that it is of Souslin type.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 11 , Issue 3 , December 1974 , pp. 395 - 411
Copyright
Copyright © Australian Mathematical Society 1974

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