Geodesic
Representation theorem for convex effect algebras
Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) no. 4, pp. 645-659 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 46A40, 46N50, 52A01, 81P10, 81R10, 82B03
Keywords: effect algebras; convex structures; ordered linear spaces 
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     title = {Representation theorem for convex effect algebras},
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Gudder, S.; Pulmannová, S. Representation theorem for convex effect algebras. Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) no. 4, pp. 645-659. http://geodesic.mathdoc.fr/item/CMUC_1998_39_4_a1/