Journal of Convex Analysis 17 (2010), No. 1, 229--240
Copyright Heldermann Verlag 2010
Measurability and Selections of Multi-Functions in Banach Spaces
Bernardo Cascales
Dep. de Matemáticas, Universidad de Murcia, 30100 Espinardo-Murcia, Spain
beca@um.es
Vladimir Kadets
Dept. of Mechanics and Mathematics, Kharkov National University, pl. Svobody 4, 61077 Kharkov, Ukraine
vova1kadets@yahoo.com
José Rodríguez
Dep. de Matemáticas, Universidad de Murcia, 30100 Espinardo-Murcia, Spain
joserr@um.es
We study the existence of measurable selectors for multi-functions whose values are weakly compact subsets of a Banach space. On one hand, we characterize multi-functions having strongly measurable selectors. On the other hand, we prove that every scalarly measurable multi-function admits scalarly measurable selectors. No separability assumptions are required for the range spaces.
Keywords: Multi-function, measurable selector.
MSC: 28B05, 28B20, 46G10
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