English

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 σ\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 EE can be extended to a state on E.E. 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}
}
R2 v1 2026-06-21T15:17:35.732Z