The convex generation of convex Borel sets in locally convex spaces

Abstract

In [3] it was proved that every convex Borel (= Baire) set in a finite dimensional real Banach space can be obtained, starting from the closed (or compact) convex sets, by the iteration of countable increasing unions and countable decreasing intersections.In §2 of this note we define some concepts of the descriptive theory of convex sets in locally convex spaces. We prove several theorems, which are analogous to the standard theorems of the descriptive theory of sets in topological spaces.