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Representation theorem for convex effect algebras

Stanley P. GudderSylvia Pulmannová — 1998

Commentationes Mathematicae Universitatis Carolinae

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.

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