The Lattice and Simplex Structure of States on Pseudo Effect Algebras

Details The Lattice and Simplex Structure of States on Pseudo Effect Algebras The Lattice and Simplex Structure of States on Pseudo Effect Algebras

2010-09-04

arxiv.org/abs/1009.0837v1

Mathematics

Functional Analysis

Scientific paper

We study states, measures, and signed measures on pseudo effect algebras with some kind of the Riesz Decomposition Property, (RDP). We show that the set of all Jordan signed measures is always an Abelian Dedekind complete $\ell$-group. Therefore, the state space of the pseudo effect algebra with (RDP) is either empty or a nonempty Choquet simplex or even a Bauer simplex. This will allow represent states on pseudo effect algebras by standard integrals.

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