The problem of characterizing derivatives revisited

“It will be noticed . . . we have adopted as one of our assumptions the condition that the integrand should be a differential coefficient with respect to one of the variables . . . In the present state of our knowledge we cannot give any but very special sets of sufficient conditions that a function should have the property of being a differential coefficient, so that the introduction of a condition of this form is not often of direct use in practice. Its importance in theory is, however, not affected by these considerations, and it has on other grounds seemed to me desirable, that, when we are concerned with a neighborhood, it is the fact of a function being a differential coefficient, and not its continuity, that we usually require.”