Observables on σ-MV algebras and σ-lattice effect algebras

Effect algebras were introduced as abstract models of the set of quantum effects which represent sharp and unsharp properties of physical systems and play a basic role in the foundations of quantum mechanics. In the present paper, observables on lattice ordered σ-effect algebras and their "smearings" with respect to (weak) Markov kernels are studied. It is shown that the range of any observable is…