A measurable selection theorem for compact-valued maps

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.