REPRESENTATION OF STATES ON EFFECT-TRIBES AND EFFECT ALGEBRAS BY INTEGRALS
Anatolij Dvurečenskij · 2010
We describe σ-additive states on effect-tribes by integrals. Effect-tribes are monotone σ-complete effect algebras of functions where operations are defined pointwise. Then we show that every state on an effect algebra is an integral through a Borel regular probability measure. Finally, we show that every σ-convex combination of extremal states on a monotone σ-complete effect algebra is a Jauch–Piron state.