Abstract
A general algebraic system M is considered with two binary operations. The family of all measurable functions with values in the unit interval is a motivating example. A state is a morphism from M to the unit interval, an observable is a morphism from the family of Borel sets to M. A joint distribution of two observables is constructed. It is applied for the construction of the sum of observables and for a representation of conditional probability.
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Riečan, B. On the Joint Distribution of Observables. Foundations of Physics 30, 1679–1686 (2000). https://doi.org/10.1023/A:1026402301407
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DOI: https://doi.org/10.1023/A:1026402301407