The class \(I_0\) on abstract structures (Q1585958)

A classical fact of the arithmetics of the semigroup of probability measures on the real line \({\mathbb R}\) is the following result of Khinchin: Every probability measure on \({\mathbb R}\) which has no indecomposable factors is infinitely divisible. Examples show that there exist infinitely divisible probability measures which have indecomposable factors. It is well-known that a large number of `reach' semigroups possess the same property: The class \(I_0\) of all elements without indecomposable factors is strictly included in the class of infinitely divisible elements of the semigroup. The authors provide three more examples: convex cones, \(q\)-probability and statistical experiments.