Abstract
The main theorem of this paper establishes the existence of measurable selections for compact-valued multifunctions whose range space is a regular Hausdorff space which need neither be metrizable nor satisfy any restriction on its weight. It is shown that the selection theorems of Sion [16], Hasumi [10], and one of the author (cf. [8]) are immediate consequences of this general result. Moreover some new results concerning Borel and Baire property selections for upper semi-continuous compact-valued maps are deduced.
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Graf, S. A measurable selection theorem for compact-valued maps. Manuscripta Math 27, 341–352 (1979). https://doi.org/10.1007/BF01507290
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DOI: https://doi.org/10.1007/BF01507290