Carathéodory selections and the Scorza Dragoni property
type: Item
instance of: scholarly article
title: Carathéodory selections and the Scorza Dragoni property
zbMATH Open document ID: 0649.28011
DOI: 10.1016/0022-247X(87)90128-4
author: Karel Prikry
author: Zvi Artstein
published in: Journal of Mathematical Analysis and Applications
publication date: 1987-01-01T00:00:00Z
review text: The authors state first the following Scorza Dragoni type result for multifunctions. Let T be a separable metric and complete space and let \(\mu\) be a finite measure on T. Let X be a separable complete metric space equipped with its Borel structure. Let F be a multifunction from \(T\times X\) taking values in X such that F is measurable and such that \(F(t,\cdot)\) is lower semicontinuous on X for each fixed \(t\in T.\) Then, for every \(\epsilon >0,\) there exists a compact set \(K\subset T\) with \(\mu (T\setminus K)\leq \epsilon\) and such that \(F|_{K\times X}\) is lower semicontinuous. Application to the existence of Carathéodory selection is given and the authors show that the condition of measurability with respect to the variables \((t,x)\) cannot be dropped. Note of the reviewer: The main result given by the authors is a consequence of a more general result published by the reviewer in Trav. Semin. d'Anal. Convexe, Vol. 6, Montpellier 1976, Exposé No.6 (1976; Zbl 0356.46045) and the approach to reduce the problem of finding a Carathéodory selection to the problem of finding continuous selection for a lower semi continuous mapping is also exploited in this previous paper by the reviewer.
Mathematics Subject Classification ID: 28B20
Mathematics Subject Classification ID: 28C05
zbMATH DE Number: 4059761
zbMATH Keywords: Scorza Dragoni type result for multifunctions
zbMATH Keywords: Carathéodory selection
zbMATH Keywords: continuous selection
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4059761