Complex-Valued Stable Measures and Their Domains of Attraction

摘要

One of the old and basic problems of probability theory is the determination of the limit distributions of sums of independent random variables. Very little seems to be known about the same analytic problem stated for the bigger class of signed measures rather than for probability measures. The subject of this paper is the investigation of this more general case. On the one hand, it turns out that the possible limit measures are a substitute for idempotent measures on the real line. On the other hand, one obtains an extension of the probability case which is now naturally embedded in a more general framework. (Author)