States on pseudo effect algebras and integrals

Details States on pseudo effect algebras and integrals States on pseudo effect algebras and integrals

2010-08-11

arxiv.org/abs/1008.1974v1

Mathematics

Functional Analysis

Scientific paper

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 $\sigma$-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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