Generalization of the Fundamental Theorem on Subadditive Functions

Source abstract

Statement of results. Let g(x) be a given real finite function of a real variable x . Let F(g) denote the class of all real Lebesgue-measurable and finite (though possibly unbounded) functions f(x) which satisfy where η may depend upon f Let F * denote the class of all real f(x) such that exists and satisfies − ∞ ≤ l <+∞.