Let ƒ be a nonincreasing function defined on [0,1]. Under standard regularity conditions, we derive the asymptotic distribution of the supremum norm of the difference between ƒ and its Grenander-type estimator on sub-intervals of [0,1]. The rate of convergence is found to be of order (n/log n)^−1/3 and the limiting distribution to be Gumbel. @en