Every State on Interval Effect Algebra is Integral
Functional Analysis
2015-05-18 v1
Abstract
We show that every state on an interval effect algebra is an integral through some regular Borel probability measure defined on the Borel -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 can be extended to a state on Our method represents also every state on the set of effect operators of a Hilbert space as an integral
Cite
@article{arxiv.1005.0171,
title = {Every State on Interval Effect Algebra is Integral},
author = {Anatolij Dvurečenskij},
journal= {arXiv preprint arXiv:1005.0171},
year = {2015}
}