Finitely subadditive outer measures, finitely superadditive inner measures and their measurable sets - P. D. Stratigos (International Journal of Mathematics and Mathematical Sciences)
Consider any set X. A finitely subadditive outer measure on P(X) is defined to be a function v from P(X) to R such that v(ϕ)=0 and v is increasing and finitely subadditive. A finitely superadditive inner measure on P(X) is defined to be a function p from P(X) to R such that p(ϕ)=0 and p is increasing and finitely superadditive (for disjoint unions) (It is to be noted that every finitely superadditive inner measure on P(X) is countably superadditive).