Abstract
We consider a discrete time version of the dynamic programming inequalities associated with the optimal stopping of a deterministic process. Their maximum solutions are shown to converge uniformly, as the discre tization step δt 0+,to the maximum solution of the continuous time formulation. A constructive proof of a result of J.L. Menaldi ([8]) on the existence of a Lipschitz solution of a 1st order variational inequality is also given.