A central limit theorem for empirical processes

The empirical measure P n for independent sampling on a distribution P is formed by placing mass n −1 at each of the first n sample points. In this paper, n ½ ( P n − P ) is regarded as a stochastic process indexed by a family of square integrable functions. A functional central limit theorem is proved for this process. The statement of this theorem involves a new form of combinatorial entropy, definable for classes of square integrable functions.