Differences of Slowly Varying Functions

We characterize a class OPql of nondecreasing slowly varying functions with the property that if the difference L1yL2 of two functions from this class is nondecreasing, then it is slowly varying. The class OPql is the restriction to nondecreasing functions of the class OPg , 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 1rlog t.