Characterizations of Outer Measures Associated with Lattice Measures

  title={Characterizations of Outer Measures Associated with Lattice Measures},
  author={P. Hsu},
Let ν be a finite countably subadditive outer measure defined on all subsets of a set X, take a collection C of subsets of X containing X and ∅, we derive an outer measure ρ using ν on sets in C. By applying this general framework on two special cases in which ν = μ′′, one where μ ∈ Mσ(L) and the other where μ ∈ Mσ(L1), L1 ⊆ L2 being lattices on a set X, we obtain new characterizations of the outer measure μ′′. These yield useful relationships between various set functions including μi, μj… CONTINUE READING

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