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

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.


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
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