The Central Limit Problem in the General Case

Abstract

After the treatment of the embedding problem in Chapter III and the problem of canonical representation of continuous convolution semigroups in Chapter IV, the presentation of the central limit problem can be considered as the culmination of the development within the framework of our theory. Many facts discussed at an earlier stage will be combined here for a detailed study of Poisson and Gauss measures on an arbitrary locally compact group as well as for the study of the convergence behavior of triangular systems of probability measures in the sense of a Lindeberg-Feller central limit theorem.