States on Pseudo Effect Algebras and Integrals |
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Authors: | Anatolij Dvurečenskij |
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Affiliation: | 1. Mathematical Institute, Slovak Academy of Sciences, ?tefánikova 49, 814 73, Bratislava, Slovakia
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Abstract: | We show that every state on an interval pseudo effect algebra E satisfying an appropriate version of the Riesz Decomposition Property (RDP for short) is an integral through a regular Borel probability measure defined on the Borel σ-algebra of a Choquet simplex K. In particular, if E satisfies the strongest type of RDP, the representing Borel probability measure can be uniquely chosen to have its support in the set of the extreme points of K. |
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