International Journal of Theoretical Physics

, Volume 38, Issue 12, pp 3179–3187 | Cite as

Convex Structures and Effect Algebras

  • Stanley Gudder


Effect algebras have important applications inthe foundations of quantum mechanics and in fuzzyprobability theory. An effect algebra that possesses aconvex structure is called a convex effect algebra. Our main result shows that any convex effectalgebra admits a representation as a generating initialinterval of an ordered linear space. This result isanalogous to a classical representation theorem for convex structures due to M. H. Stone. We alsogive a relationship between a convex effect algebra anda statistical model called a convex effect-statespace.


Field Theory Statistical Model Elementary Particle Quantum Field Theory Quantum Mechanic 
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Copyright information

© Plenum Publishing Corporation 1999

Authors and Affiliations

  • Stanley Gudder

There are no affiliations available

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