Let F be a collection of distributions on Rd. A functional T defined on F is Gteaux differentiable at G E F if and only if 14 Chapter 5. Estimation in Nonparametric Models 223 there is a linear functional Lg on D= {c(G1-G2): c ER, G; EF, j = 1, 2} (i.e., LG(C141+c242) = cLG(41)+c2LG(42) for any A; E D and C; E R) such that AED and G+TA E F imply [T(G+TA) T(G)_ lim - LG(A) = 0. t->0 t = Assume that the functional Lf is continuous in the sense that || A; -A||20+ 0 implies LF(4;) + LF(A), where D E D, D; E D, and || D|| 20 supx|D(x) for any D E D is the sup-norm. Show that f(x) = LF(Oz - F) is a bounded function of x, where 8is the degenerated distribution at x