Convexity theories IV. Klein-Hilbert parts in convex modules

The Klein-Hilbert part relation, which was introduced by Gleason in function algebras and investigated for convex subsets of real vector spaces by Bear and Bauer in [3], [5], [2], is defined for convex modules. It turns out that all results that were proved for convex sets can also be proved for convex modules, which constitute the algebraic theory generated by convex sets and which have a close connection to physics and mathematical economics.