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Some results on density of extreme selections for measurable multifunctions. (English) Zbl 0612.28007
In this paper the author deals with measurable multifunctions F from A into \(2^ E\) where (A,\({\mathcal A},m)\) is a complete measure space with m nonnegative, finite and nonatomic, and where E is a locally convex Suslin space. Under different specific hypotheses on A and E the author establishes density properties of the set of measurable selections of F in the set of measurable selections of \(cl co F,\) avoiding the assumptions of integrability on F and choosing suitable topologies in which the density is considered. The main results generalize and extend analogous theorems of Lyapunov’s type given by different authors in these last twenty years.
Reviewer: P.Pucci

MSC:
28B20 Set-valued set functions and measures; integration of set-valued functions; measurable selections
54C65 Selections in general topology
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