On Constructing Finite, Finitely Subadditive Outer Measures, and Submodularity

Abstract EN

Given a nonempty abstract set X, and a covering class ?, and a finite, finitely subadditive outer measure ν, we construct an outer measure ν¯ and investigate conditions for ν¯ to be submodular.

We then consider several other set functions associated with ν and obtain conditions for equality of these functions on the lattice generated by ?.

Lastly, we describe a construction of a finite, finitely subadditive outer measure given an arbitrary family of subsets, ℬ, of X and a nonnegative, finite set function τ defined on ℬ.