Approximating families for lattice outer measures on unsharp quantum logics

Abstract The aim of the present paper is to study lattice outer measures on an unsharp quantum logic, viz. a difference poset P associated with a monotone function μ defined on a sub-difference poset L of P and an approximating family in L. Having proved a number of fundamental properties, relationships among these outer measures and eventually among corresponding families of measurable elements of P are investigated.