Observables on hypergraphs |
| |
Authors: | S. P. Gudder G. T. Rüttimann |
| |
Affiliation: | (1) Department of Mathematics and Computer Science, University of Denver, 80208 Denver, Colorado |
| |
Abstract: | Observables on hypergraphs are described by event-valued measures. We first distinguish between finitely additive observables and countably additive ones. We then study the spectrum, compatibility, and functions of observables. Next a relationship between observables and certain functionals on the set of measures M(H) of a hypergraph H is established. We characterize hypergraphs for which every linear functional on M(H) is determined by an observable. We define the concept of an effect and show that observables are related to effect-valued measures. Finally, we define operational transformations from M(H) to itself and show that they can be described as a certain combination of effects.On leave from University of Berne, Institute of Mathematical Statistics, Sidlerstrasse 5, CH-3012 Berne, Switzerland. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|