We study discretization in classes of integro-differential equationswhere the functions aj（t）, 1 ≤ j ≤n, are completely monotonic on （0, ∞） and locally integrable, but not constant. The equations are discretized using the backward Euler method in combination with order one convolution quadrature for the memory term. The stability properties of the discretization are derived in the weighted 11 （p; 0, ∞） norm, where p is a given weight function. Applications to the weighted l^1 stability of the numerical solutions of a related equation in Hilbert space are given.
