Decompositions of Riesz space-valued measures on orthomodular posets

Rok, strany: 1993, 229 - 239

We present a decomposition theorem showing that any positive finitely additive measure defined on an orthomodular poset attaining values in a Dedekind complete normed Riesz space can be expressed as a sum of two finitely additive measures, where the first one belongs to a given cone of measures, and the second one is singular with respect to the cone. As corollaries we obtain Yosida-Hewitt-type decompositions giving cones of $σ$-additive measures, completely additive measures, $P$-regular measures, Lebesgue-type-decomposition, and Aarnes decomposition on inner product spaces.

ISO 690:

De Lucia, P., Dvurečenskij, A. 1993. Decompositions of Riesz space-valued measures on orthomodular posets. In Tatra Mountains Mathematical Publications, vol. 2, no.1, pp. 229-239. 1210-3195.

APA:

De Lucia, P., Dvurečenskij, A. (1993). Decompositions of Riesz space-valued measures on orthomodular posets. Tatra Mountains Mathematical Publications, 2(1), 229-239. 1210-3195.