Dorninger, D., & Länger, H. (2018). Structural properties of algebras of S-probabilities. Mathematica Slovaca, 68(3), 485–490. https://doi.org/10.1515/ms-2017-0118
E104-01 - Forschungsbereich Algebra E104 - Institut für Diskrete Mathematik und Geometrie
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Journal:
Mathematica Slovaca
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ISSN:
0139-9918
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Date (published):
2018
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Number of Pages:
6
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Publisher:
WALTER DE GRUYTER GMBH
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Peer reviewed:
Yes
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Keywords:
General Mathematics
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Abstract:
Let S be a set of states of a physical system. The probabilities p(s) of the occurrence of an event when the system is in different states s ∈ S define a function from S to [0, 1] called a numerical event or, more precisely, an S-probability. A set of S-probabilities comprising the constant functions 0 and 1 which is structured by means of the addition and order of real functions in such a way that an orthomodular partially ordered set arises is called an algebra of S-probabilities, a structure significant as a quantum-logic with a full set of states. The main goal of this paper is to describe algebraic properties of algebras of S-probabilities through operations with real functions. In particular, we describe lattice characteristics and characterize Boolean features. Moreover, representations by sets are considered and pertinent examples provided.
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Research Areas:
außerhalb der gesamtuniversitären Forschungsschwerpunkte: 100%