Concerning the condition of additivity in quantum field theory

The condition of additivity for local von Neumann algebras is discussed within the framework of local quantum field theory. It is shown that this condition holds for algebras of observables associated with wedge-shaped regions in Minkowski space-time if the system of local algebras is associated with a local quantum field in a weak sense. And under somewhat stronger conditions additivity is shown to hold for arbitrary regions for the algebras of a certain minimal net generated by the quantum field