States on pseudo effect algebras and integrals
Abstract
We show that every state on an interval pseudo effect algebra E satisfying some kind of the Riesz Decomposition Properties (RDP) 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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