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 $\sigma$-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 $K.$

References in corpus (1)

• Every State on Interval Effect Algebra is Integral

Cited by in corpus (2)

• Kite Pseudo Effect Algebras
• The Lattice and Simplex Structure of States on Pseudo Effect Algebras