Finitely subadditive and countably subadditive outer measures

Abstract

Results are given comparing countably subadditive (csa) outer measures and finitely subadditive (fsa) outer measures, especially relating to regularity and measurability conditions such as (*) condition:A setE (of an arbitrary setX),\(X \supseteq E\) is μ measurable (μ an outer measure),EeSμ (the collection of μ measurable sets) iff μ(X)=μ(E)+μ(E′). Specific examples are given contrasting csa and fsa outer measures. In particular fsa and csa outer measures derived from finitely additive measures defined on an algebra of sets generated by a lattice of sets, are investigated in some detail.