A note on measure extension problem of ℓ-group-valued measures

For an Abelian, Archimedean Dedekind complete lattice-ordered, weakly σ-distributive group G and an algebra Ƒ

of subsets of a set X, every positive measure μ: Ƒ→G has a unique countably additive (in order convergence) extension to σ-algebra generated by Ƒ.