Rigorous derivation of the Kirkwood–Monroe equation for small activity

We show, for small values of z, that the solution of the Kirkwood-Salsburg equation approaches, in the norm topolgy, the solution of the Kirkwood-Monroe and van Kampen equations if the potential of interaction is the Kac potential φ (x12) =γsg(γx12) and the limit γ→0 is taken. We have to assume that the function g is bounded and absolutely integrable and that Σi≠j (γxij) ⩾−mB (B<∞), the the sum being performed over all pairs of the m particles.