Representation theorem for convex effect algebras. (English) Zbl 1060.81504

Gudder, S.; Pulmannová, S.

Commentat. Math. Univ. Carol. 39, No. 4, 645-659 (1998).

Summary: Effect algebras have important applications in the foundations of quantum mechanics and in fuzzy probability theory. An effect algebra that possesses a convex structure is called a convex effect algebra. Our main result shows that any convex effect algebra admits a representation as a generating initial interval of an ordered linear space. This result is analogous to a classical representation theorem for convex structures due to M. H. Stone.

MSC:

81P10	Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
46A40	Ordered topological linear spaces, vector lattices
46N50	Applications of functional analysis in quantum physics
52A01	Axiomatic and generalized convexity

Keywords:

effect algebras; convex structures; ordered linear spaces