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On sublinear functionals defined on the space of Bochner integrable functions. (English. Russian original) Zbl 0828.46037

Sib. Math. J. 35, No. 1, 178-188 (1994); translation from Sib. Mat. Zh. 35, No. 1, 194-206 (1994).
Summary: We study sublinear functionals that are defined on the space of Bochner integrable functions and possess the properties of decomposition and scalar compactness. We give an integral representation for the functionals. Such functionals are used in proving theorems on existence of continuous selections for a family of lower semicontinuous multivalued mappings with decomposable closed nonconvex values in the space of Bochner integrable functions.

MSC:

46E40 Spaces of vector- and operator-valued functions
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
54C65 Selections in general topology
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