Convex and linear effect algebras

It is shown that convex effect algebras arise naturally in the description of a physical statistical system. An effect algebra that is a convex subset of a real linear space is called a linear effect algebra and it is demonstrated that any convex effect algebra is affinely isomorphic to a linear effect algebra. Convex effect algebras that possess separating and order determining state spaces are characterized. It is shown that an effect algebra P is imbeddable in an interval of an order unit space if and only if the state space of P is order determining. Sharp and extreme elements of convex effect algebras are studied and compared. An alternative definition of a convex effect algebra called a CE-algebra is considered and MV-algebras are discussed.