Geodesic
Joint continuous selections of multivalued mappings with nonconvex values, and their applications
Sbornik. Mathematics, Tome 73 (1992) no. 2, pp. 319-339

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A continuous version of a theorem of Lyapunov on convexity for measures with values in a Banach space is proved, and then used to obtain two results on the existence of a common continuous selection of finitely many multivalued mappings with values in a space of Bochner-integrable functions. These results are applied to the investigation of properties of solutions of differential inclusions with $m$-accretive operators. 
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     author = {V. V. Goncharov and A. A. Tolstonogov},
     title = {Joint continuous selections of multivalued mappings with nonconvex values, and their applications},
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V. V. Goncharov; A. A. Tolstonogov. Joint continuous selections of multivalued mappings with nonconvex values, and their applications. Sbornik. Mathematics, Tome 73 (1992) no. 2, pp. 319-339. http://geodesic.mathdoc.fr/item/SM_1992_73_2_a1/