Abstract
We propose a simple set-theoretic model of a generalized probability spaceadmitting intrinsic incompatible events and incompatible observables. It is acoproduct in the category D of D-posets and D-homomorphisms each factor ofwhich is a classical Kolmogorovian probability space. Since classical events,random functions, and probability measures can be treated within D in a canonicalway, the Kolmogorovian model becomes a special case. We show that σ-additivityand other σ-notions can be replaced in a natural way by sequential continuity.
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Frič, R. On Observables. International Journal of Theoretical Physics 39, 677–686 (2000). https://doi.org/10.1023/A:1003693922379
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DOI: https://doi.org/10.1023/A:1003693922379