Absolute continuity of states on concrete logics

By concrete logic we mean a quantum logic which is set-representable, and b y Vitali-Hahn-Saks logic (VHS-logic) we mean a concrete logic for which the Vitali-Hahn-Saks theorem holds true. In this note we investigate the size of the class of VHS-logics, showing among others that each concrete logic c an be concretely enlarged to a VHS-logic as well as to a non-VHS-logic.