On the Minimal Solution of the Problem of Primitives

We characterize the primitives of the minimal extension of the Lebesgue integral which also integrates the derivatives of differentiable functions (called the Cintegral). Then we prove that each BV function is a multiplier for the C-integral and that the product of a derivative and a BV function is a derivative modulo a Lebesgue integrable function having arbitrarily small L1-norm.