Every state on interval effect algebra is integral
Anatolij Dvurečenskij · Journal of Mathematical Physics · 2010
We show that every state on an interval effect algebra is an integral through some regular Borel probability measure defined on the Borel σ-algebra of a compact Hausdorff simplex. This is true for every effect algebra satisfying Riesz decomposition property or for every many valued (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.