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

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

2010-06-10

arxiv.org/abs/1006.1958v1

Mathematics

Functional Analysis

20 pages

Scientific paper

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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