Every State on Interval Effect Algebra is Integral

Abstract

We show that every state on an interval effect algebra is an integral through some regular Borel probability measure defined on the Borel $\sigma$-algebra of a compact Hausdorff simplex. This is true for every effect algebra satisfying (RDP) or for every MV-algebra. In addition, we show that each state on an effect subalgebra of an interval effect algebra $E$ can be extended to a state on $E.$ Our method represents also every state on the set of effect operators of a Hilbert space as an integral

Cited by in corpus (6)

• Cohomology of Effect Algebras
• The Lattice and Simplex Structure of States on Pseudo Effect Algebras
• States on pseudo effect algebras and integrals
• A characterisation of ordered abstract probabilities
• The three types of normal sequential effect algebras
• Representation of States on Effect-Tribes and Effect Algebras by Integrals