Representation of States on Effect-Tribes and Effect Algebras by Integrals

Abstract

We describe $\sigma$-additive states on effect-tribes by integrals. Effect-tribes are monotone $\sigma$-complete effect algebras of functions where operations are defined by points. Then we show that every state on an effect algebra is an integral through a Borel regular probability measure. Finally, we show that every $\sigma$-convex combination of extremal states on a monotone $\sigma$-complete effect algebra is a Jauch-Piron state.

20 pages

References in corpus (1)

• Every State on Interval Effect Algebra is Integral

Cited by in corpus (2)

• Smearing of Observables and Spectral Measures on Quantum Structures
• States and synaptic algebras