The support of a uniform semigroup valued measure (Q868732)

At the very outset, the authors expose the basic theory of partial Abelian monoids with several examples and a brief presentation of some of its substructures: effect algebras, orthoalgebras, orthomodular posets, orthomodular lattices and Boolean algebras. The authors deal with characterization theorems and several properties of such structures to use them subsequently. In the next phase, the authors give a basic theory of uniform semigroups and some pertinent classes of measures which are uniform semigroup valued. In the final section, the authors bring the concept of Jauch-Piron measure and support of a measure; examples have been provided. The main results of the paper consist of two theorems: the first one describes the conditions under which a measure is a completely additive Jauch-Piron measure; the second one gives a condition under which a positive Jauch-Piron measure has a support.