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arXiv · 1006.1958

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

Anatolij Dvurečenskij
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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.

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Anatolij Dvurečenskij. 2010-06-10. Representation of States on Effect-Tribes and Effect Algebras by Integrals. https://doi.org/10.1016/s0034-4877(11)80011-x

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