The extension of measures on D-lattices

摘要

A lattice ordered group valued measure is extended from a D-lattice into a σ-complete D-lattice. A D-lattice is a lattice with a greatest element 1 and a smallest element 0 endowed with an order-compatible operation, called a difference, which satisfies a list of axioms. The result generalizes the classical result known for measures on Boolean algebras.