Title: Variants on the Berz sublinearity theorem,
Abstract: We consider variants on the classical Berz sublinearity theorem, using only
DC, the Axiom of Dependent Choices, rather than AC, the Axiom of Choice which
Berz used. We consider thinned versions, in which conditions are imposed on
only part of the domain of the function -- results of quantifier-weakening
type. There are connections with classical results on subadditivity. We close
with a discussion of the extensive related literature.