Generalizations of a theorem of Arrow, Barankin, and Blackwell in topological vector spaces

摘要

It is proved that the density theorem of Arrow, Barankin, and Blackwell holds in a topological vector space equipped with a weakly closed convex cone to admit strictly positive continuous linear functionals. Moreover, several local versions of the Arrow, Barankin, and Blackwell theorem are given. [References: 18]