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arXiv · 1008.1974

States on pseudo effect algebras and integrals

Anatolij Dvurecenskij
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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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Anatolij Dvurecenskij. 2010-08-11. States on pseudo effect algebras and integrals. https://doi.org/10.1007/s10701-011-9537-4

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