On the Lower Derivate of a Set Function
Washek Frank Pfeffer · Canadian Journal of Mathematics · 1968
In (5), the following theorem was proved in a very general setting: (1) An additive set function is non-negative whenever its lower derivative is non-negative. For a continuous additive function of intervals, theorem (1) can be improved as follows: (2) A continuous additive set function is non-negative whenever its lower derivative is non-negative except, perhaps, on a countable set.