## Additive and Non-additive Set Functions |

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absolutely continuous absolutely integrable function abstract Boolean ring additive functions additive set function atom of CL Boolean algebra Canonical decomposition carrier carries f Chapter collection of sets defined denote the number deviation of f directed limit directed sets empty set EXAMPLE f e F f is absolutely f is additive f is integrable finite collection finite deviation finite number finite ring finite subring formula of Theorem functions of finite functions of intervals ground partition Hence imputation operators inclusion function infinite Lebesgue measure Let f monotone non-additive set functions non-empty set non-measurable sets non-negative norm number of atoms omit the proof ordered by inclusion outer measure partially ordered partition function partition function tt partition tree positive measure real numbers refinement ring CL set function f e spectrum square-free integers step-functions Stieltjes integral subadditive function subcollection subsets superadditive function t(tt Theorem 12 Theorem 27 Theorem 34 theory