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.
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On leave from University of Berne, Institute of Mathematical Statistics, Sidlerstrasse 5, CH-3012 Berne, Switzerland.
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Gudder, S.P., Rüttimann, G.T. Observables on hypergraphs. Found Phys 16, 773–790 (1986). https://doi.org/10.1007/BF00735379
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DOI: https://doi.org/10.1007/BF00735379