We give examples which show the necessity of employing weight functions in order to have (a) and (b), and prove the optimality of the weight function classes which we make use of. We describe classes of weight functions which enable us to establish the (a) strong uniform-over-$[0, \infty)$ consistency and (b)weak uniform-over-$[0, \infty)$ approximation of MRL processes. In this exposition we study MRL processes over the whole positive half-line $[0, \infty)$. They obtained results holding true over fixed and expanding compact subintervals of $[0, \infty)$. Yang and Hall and Wellner initiated investigations of the asymptotic uniform behaviour of mean residual life (MRL) processes.
