  Probability maps are additive and normalised maps taking values in the unit
interval of a lattice ordered Abelian group. They appear in theory of affine
representations and they are also a semantic counterpart of Hajek's probability
logic. In this paper we obtain a correspondence between probability maps and
positive operators between certain Riesz spaces, which extends the well-known
representation theorem of real-valued MV-algebraic states by positive linear
functionals. When the codomain algebra contains all continuous functions, the
set of all probability maps is convex, and we prove that its extreme points
coincide with homomorphisms. We also show that probability maps can be viewed
as a collection of states indexed by maximal ideals of a codomain algebra and
we characterise this collection in special cases.
