Additivity of integrals on generalized measure spaces
A generalized measure space is a triple (\(\Omega\),\({\mathcal C},\mu)\) where \(\Omega\) is a set of \({\mathcal C}\), a \(\sigma\)-class of subsets of \(\Omega\) closed with respect to disjoint countable unions and complementation and \(\mu\) a measure on \({\mathcal C}\). While in the classical measure theory additivity of integral is an obvious and fundamental result, it is not so in the generalized measure spaces. In general the integral in this case is not additive. The question of the additivity in the case of simple functions is solved in the reviewed paper in a positive way.
scientific article; zbMATH DE number 4012955