Bressan, Alberto; Colombo, Giovanni Extensions and selections of maps with decomposable values. (English) Zbl 0677.54013 Stud. Math. 90, No. 1, 69-86 (1988). Let X be a separable metric space, E - a Banach space, \(\mu\)- a nonatomic probability measure on a space T, and \(L^ 1\)- the Banach space of \(\mu\)-integrable functions u: \(T\to E\). A set \(K\subset L^ 1\) is decomposable if \(u\cdot \chi_ A+v\cdot \chi_{T\setminus A}\in K\) for any \(\mu\)-measurable set \(A\subset T\) and all \(u,v\in K\). The property of decomposability is a good substitute for convexity [cf. C. Olech, Proc. Conf. Catanica/Italy 1983, lect. Notes Math. 1091, 193-205 (1984; Zbl 0592.28008)]. Using this property the authors prove analogues of three theorems by Dugundji, Cellina and Michael on extensions and selections of (multivalued) maps. Reviewer: K.Nikodem Cited in 13 ReviewsCited in 176 Documents MSC: 54C65 Selections in general topology 54C20 Extension of maps Citations:Zbl 0592.28008 PDFBibTeX XMLCite \textit{A. Bressan} and \textit{G. Colombo}, Stud. Math. 90, No. 1, 69--86 (1988; Zbl 0677.54013) Full Text: DOI EuDML