Vector Lattices Associated with Ordered Vector Spaces

Let V be a real, Archimedian ordered, vector space, whose positive cone V ⁺ satisfies V =  V ⁺ – V ⁺. To V we associate a Dedekind complete vector lattice W containing V (by abuse of notation). In the case when V has an order unit the determination of W is already known. Let W₀ ì W{W_0 \subset W} be the vector lattice generated by V. We study W ₀ in the case when the cone C of all positive linear forms on V separates the elements of V. The determination of W ₀ involves the extreme rays of C. We determine the cone of positive linear forms on W ₀ in terms of conical measures on C.