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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.

Approximating families for lattice outer measures on unsharp quantum logics