Smearing of Observables and Spectral Measures on Quantum Structures

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 algebras 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 is its spectral measure.

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