NOTE ON THE CONTINUATION OF INFINITELY DIVISIBLE DISTRIBUTIONS AND CANONICAL MEASURES

We consider the question, to what extent an infinitely divisible distr ibution function on R+ is determined by its values on an interval star ting at zero, or by the values of its canonical measure on such an int erval. These questions are considered in the book by Rossberg ct al. ( 1985). Our results extend parts of their work. These results are appli ed to the continuation of constant multiples of infinitely divisible d istribution functions and to the distribution of subordinators.