ABSTRACT

The DeMoivre-Laplace Integral Limit Theorem has served as a basic source for a number of investigations of fundamental significance both for the theory of probability and for its various applications to the natural sciences, engineering and economics. The problem thus arises of investigating the laws governing the behavior of the value of the sums of a larger number of independent random variables each of which has only a minor effect on the entire sum. In order to study such sums of a very large but finite number of terms, one instead considers a sequence of sums having an increasing number of terms and then takes into account corresponding limit distribution functions of the sums. This sort of passing from a finite formulation of a problem to limit is very typical in modem mathematics and in many branches of the natural sciences.