Note on the continuation of infinitely divisible distributions and canonical measures

We consider the question, to what extent an infinitely divisible distribution function on is determined by its values on an interval starting at zero, or by the values of its canonical measure on such an interval. These questions are considered in the book by Rossberg et al. (1985). Our results extend parts of their work. These results are applied to the continuation of constant multiples of infinitely divisible distribution functions and to the distribution of subordinators.