Differences of slowly varying functions

Abstract

We characterize a class OΠ+l of nondecreasing slowly varying functions with the property that if the difference L1-L2 of two functions from this class is nondecreasing, then it is slowly varying. The class OΠ+l is the restriction to nondecreasing functions of the class OΠg, well known in the theory of regularly varying functions, where the auxiliary function g is taken to be a slowly varying nondecreasing function l with remainder term 1/logt.