Generalized monotone convergence and Radon–Nikodym theorems
Stanley Gudder, Julia E Zerbe · Journal of Mathematical Physics · 1981
A measure and integration theory is presented in the quantum logic framework. A generalization of the monotone convergence theorem is proved. Counterexamples are used to show that the dominated convergence theorem, Fatou’s lemma, Egoroff’s theorem, and the additivity of the integral do not hold in this framework. Finally, a generalization of the Radon–Nikodym theorem is proved.