Note on Newtonian Force-Fields

Abstract

Although the behaviour of Newtonian potentials inside n-dimensional distributions of mass or charge has been discussed in the sense of Lebesgue-Stieltjes integrals by various authors, the discussion of various important theorems seems to have been made only in the sense of Riemann integration, and assuming the Hälder conditions (or at least piecewise continuity) for the volume density p. We shall generalize these theorems below.