Decompositions of measures on pseudo effect algebras

Abstract

Recently, in Dvurečenskij (http://arxiv.org/submit/103087, 2011), it was shown that if a pseudo effect algebra satisfies a kind of the Riesz decomposition property (RDP), then its state space is either empty or a nonempty simplex. This will allow us to prove a Yosida–Hewitt type and a Lebesgue type decomposition for measures on pseudo effect algebra with RDP. The simplex structure of the state space will entail not only the existence of such a decomposition but also its uniqueness.