ABSTRACT
Most properties proved in this chapter can be specialized to properties for distributions on R+ or Z+. Quite often the properties thus obtained will be less informative than the ones proved earlier in Chapters II and III of this book. On the other hand, many results obtained for distributions on R+ or Z+ will not be available for distributions on R, or less generally true, or harder to prove. Since in the literature one usually deals with results for general distributions on R (the books by Feller are exceptions), these results are more easily available than those for distributions on R+ or Z+. With this in mind we will only give an outline of the rather technical proof of the Le´vy-Khintchine representation of an infinitely divisible characteristic function. It is convenient, and occasionally inevitable, to use some results from Chapters II and III; but if one is willing to accept these few results, then the present chapter can be read independent of the preceding ones.
