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Let ν be a finite countably subadditive outer measure definedon all subsets of a set X, take a collection ℂ ofsubsets of X containing X and ∅, we derive an outermeasure ρ using ν on sets in ℂ.  By applyingthis general framework on two special cases in which ν=μ″,one where μ∈Mσ() and the other where μ∈Mσ(1),1⫅2 being lattices on a setX, we obtain new characterizations of the outer measure μ″.These yield useful relationships between various set functionsincluding μi,μj,μ″, and μ′

Characterizations of outer measures associated with lattice measures