Representable Effect Algebras and Observables
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We introduce a class of monotone σ-complete effect algebras, called representable, which are σ-homomorphic images of a class of monotone σ-complete effect algebras of functions taking values in the interval [0, 1] and with effect algebra operations defined by points. We exhibit different types of compatibilities and show their connection to representability. Finally, we study observables and show situations when information of an observable on all intervals of the form (−∞, t) gives full information about the observable.
KeywordsEffect algebra Compatibility Strong-compatible Internal compatibility Monotone σ-completeness Homogeneous algebra Observable Block
The author is very indebted to anonymous referees for their careful reading and suggestions which helped to improve the readability of the paper.
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