Weak Convergence of the Empirical Characteristic Function

Let X be a real valued random variable with probability distribution function F (x) and characteristic function c (t). Let Fₙ (x) be the nth empirical distribution function associated with X and cₙ (t) the characteristic function of Fₙ (x). Necessary and sufficient conditions are obtained for the weak convergence of n cₙ (t) - c (t) on the space of continuous complex valued functions on -1/2, 1/2.