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Shape-constrained functions appear very commonly in nonparametric estimation in statistics via renewal theory and mixing of uniform distributions.In order to de termine the rate of convergence of a nonparametric estimator such as the Maximum Likelihood Estimator, one often needs to know the metric entropy estimate of these function classes.In this talk, I will present some probability techniques and recent results on entropy estimate of several shape-coustrained function classes.As a spe cific example, I will present how small deviation probability of k-times integrated Brownian motions under sup norm can be used to obtain metric entropy estimate of k-monotone functions under L(2) norm.