Geodesic
Approximation of semicontinuous multivalued mappings by continuous ones
Izvestiya. Mathematics , Tome 20 (1983) no. 3, pp. 435-448.

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Properties of semicontinuous multivalued mappings are studied that are analogous to properties of semicontinuous single-valued functions. Theorems are proved on monotone approximation of semicontinuous multivalued mappings by continuous ones, and a theorem is proved on separating a lower semicontinuous multivalued mapping from an upper semicontinuous one imbedded in it by a continuous multivalued mapping. Bibliography: 10 titles. 
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S. M. Aseev. Approximation of semicontinuous multivalued mappings by continuous ones. Izvestiya. Mathematics , Tome 20 (1983) no. 3, pp. 435-448. http://geodesic.mathdoc.fr/item/IM2_1983_20_3_a1/

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