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Zbl 0677.54013
Bressan, Alberto; Colombo, Giovanni
Extensions and selections of maps with decomposable values.
(English)
[J] Stud. Math. 90, No.1, 69-86 (1988). ISSN 0039-3223; ISSN 1730-6337/e

Let X be a separable metric space, E - a Banach space, $\mu$- a nonatomic probability measure on a space T, and $L\sp 1$- the Banach space of $\mu$-integrable functions u: $T\to E$. A set $K\subset L\sp 1$ is decomposable if $u\cdot \chi\sb A+v\cdot \chi\sb{T\setminus A}\in K$ 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. {\it 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.
[K.Nikodem]
MSC 2000:
*54C65 Continuous selections
54C20 Extension of maps on topological spaces

Citations: Zbl 0592.28008

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