Smearing of Observables and Spectral Measures on Quantum Structures

Foundations of Physics 43 (2):210-224 (2013)
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Abstract

An observable on a quantum structure is any σ-homomorphism of quantum structures from the Borel σ-algebra of the real line into the quantum structure which is in our case a monotone σ-complete effect algebra with the Riesz Decomposition Property. We show that every observable is a smearing of a sharp observable which takes values from a Boolean σ-subalgebra of the effect algebra, and we prove that for every element of the effect algebra there corresponds a spectral measure

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Effect algebras and unsharp quantum logics.D. J. Foulis & M. K. Bennett - 1994 - Foundations of Physics 24 (10):1331-1352.
Boolean Algebras.Roman Sikorski - 1966 - Journal of Symbolic Logic 31 (2):251-253.

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