Quantum logics with the Radon-Nikodym property
A \(\sigma\)-orthomodular partially ordered set L is called a logic and a probability measure on L is called a state of L, as is usual in the so- called logico-algebraic approach to the foundations of quantum mechanics. A logic is said to have the Radon-Nikodym property and is called an RN- logic if it satisfies the following condition: If s, t are states on L and s is absolutely continuous with respect to t, then there is a central observable x such that \(s(a)=\int_{a}x dt\) for any \(a\in L\). The authors study the basic properties of RN-logics, including their closedness under the formation of epimorphisms and products. It is shown also that in many cases the concrete RN logics have to be Boolean \(\sigma\)-algebras, whereas there are concrete RN logics with an aribtrary degree of noncompatibility. This result extends their previous paper [J. Math. Phys. 24, 1450 (1983tion is reliable.
scientific article; zbMATH DE number 4047716
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