Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • Multi-function
  • measurable selector

Mathematics Subject Classification

28B05, 28B20, 46G10

Suggested citation

B. Cascales, V. Kadets, J. Rodríguez. “Measurability and Selections of Multi-Functions in Banach Spaces.” Journal of Convex Analysis 17 (2010), No. 1, 229–240. https://doi.org/10.68381/jca17017

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Published by Heldermann Verlag, 2010. Rights now held by Banach Press.