A STRENGTHENED CENTRAL-LIMIT-THEOREM FOR SMOOTH DENSITIES

We consider the central limit theorem for the probability density func tion f(n)(x) of the standardized sum of independent and identically di stributed random variables with finite variance and regular probabilit y density function. By showing boundedness of different convex functio nals along the sequence {f(n)} we prove convergence in various norms t o the normal density. (C) 1995 Academic Press, Inc.