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Structural properties of algebras of $S$-probabilities

In: Mathematica Slovaca, vol. 68, no. 3
Dietmar Dorninger - Helmut M. Länger
Detaily:
Rok, strany: 2018, 485 - 490
Kľúčové slová:
algebra of $S$-probabilities, lattice properties, concrete quantum logic, infimum faithful logic, Boolean algebra
O článku:
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 $s\in S$ define a function from $S$ to $[0,1]$ called a {\em numerical event} or, more precisely, an {\em $S$-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 {\em 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.
Ako citovať:
ISO 690:
Dorninger, D., Länger, H. 2018. Structural properties of algebras of $S$-probabilities. In Mathematica Slovaca, vol. 68, no.3, pp. 485-490. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0118

APA:
Dorninger, D., Länger, H. (2018). Structural properties of algebras of $S$-probabilities. Mathematica Slovaca, 68(3), 485-490. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0118
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