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CM-Selectors for pairs of oppositely semicontinuous multivalued maps with $_{p}$ -decomposable values

Hôǹg Thái Nguyêñ; Maciej Juniewicz; Jolanta Ziemińska — 2001

Studia Mathematica

We present a new continuous selection theorem, which unifies in some sense two well known selection theorems; namely we prove that if F is an H-upper semicontinuous multivalued map on a separable metric space X, G is a lower semicontinuous multivalued map on X, both F and G take nonconvex $L_{p} (T, E)$ -decomposable closed values, the measure space T with a σ-finite measure μ is nonatomic, 1 ≤ p < ∞, $L_{p} (T, E)$ is the Bochner-Lebesgue space of functions defined on T with values in a Banach space E, F(x) ∩ G(x) ≠ ∅...

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CM-Selectors for pairs of oppositely semicontinuous multivalued maps with p -decomposable values

CM-Selectors for pairs of oppositely semicontinuous multivalued maps with $_{p}$ -decomposable values