On optimal averages
By an optimal measure we mean a set function defined on a \(\sigma\)- algebra into the interval \([0,1]\), suitably normalized, which is continuous from above and maps finite unions into finite maxima. As a natural consequence we introduced on the set of measurable functions the so-called optimal average which is a positively homogeneous, monotone increasing, subadditive and finite maximum preserving functional. This nonlinear functional seems to parallel in many ways the Lebesgue integral (or mathematical expectation): in the theory of Lebesgue integral, a good deal of fundamental theorems have each a counterpart in the theory of optimal average.
scientific article; zbMATH DE number 556297
scientific article