A selection theorem for multifunctions
Author: H. Sarbadhikari
Journal: Proc. Amer. Math. Soc. 71 (1978), 285-288
MSC: Primary 54C65; Secondary 04A20, 54A25, 54C60
MathSciNet review: 500507
Abstract: In this paper the following theorem is proved. X is any set, H is a family of subsets of X which is -additive, -multiplicative and satisfies the -WRP for some cardinal . Suppose Y is a regular Hausdorff space of topological weight such that given any family of open sets, there is a subfamily of cardinality with the same union. Let , where is the family of nonempty compact subsets of Y, satisfy for any closed subset C of Y. Then F admits a measurable selector.
Keywords: -additive family of sets, -multiplicative family of sets, -weak reduction principle, H-measurable function, selector
Article copyright: © Copyright 1978 American Mathematical Society