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Quantum measure theory. (English) Zbl 1249.81002

I the paper additivity is substituted by the following properties: 1. If \(A,B,C\) are pairwise disjoint, then \(\mu (A\cup B\cup C) =\mu (A\cup B)+\mu (A\cup C)+\mu (B\cup C)-\mu (A)-\mu (B)-\mu (C)\). 2. If \(\mu (A) = 0,\, A\cap B = \emptyset \), then \(\mu (A\cup B) = \mu (B)\). 3. If \(A\cap B = \emptyset ,\, \mu (A\cup B) = 0\), then \(\mu (A) = \mu (B)\).
Quantum measure is a continuous measure with those properties. In the paper compatibility of sets is studied and the center of a quantum measure space is characterized. Quantum measures are characterized in terms of signed product measures. The author suggests to use quantum measures for computing and predicting elementary particle masses.

MSC:

81P15 Quantum measurement theory, state operations, state preparations
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References:

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