Every State on Interval Effect Algebra is Integral

Details Every State on Interval Effect Algebra is Integral Every State on Interval Effect Algebra is Integral

2010-05-02

arxiv.org/abs/1005.0171v1

Mathematics

Functional Analysis

Scientific paper

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

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