lifting continuity properties of aggregation functions to their super- and sub-additive transformations

We investigate possible extensions of various types of continuity of aggregation functions to their super- and sub-additive transformations. more specifically, we examine lifts of classical, uniform, lipschitz and holder continuities and differentiability. the classical, uniform, and lipschitz continuities turn out to be preserved by super- and sub-additive transformations (albeit for uniform continuity and the super-additive case we prove it only in dimension one), while the holder continuity and differentiability are not.