# Convolutional roots of mixture of exponential distributions

In the reference book on infinite divisibility and generalised gamma convolution, BONDESSON, Lennart. Generalized gamma convolutions and related classes of distributions and densities. Springer Science & Business Media, 2012., page 26, the theorem 2.4.3 states :

An MED is infinitely divisible and it's convolutional roots are MED's.

Unfortunately the proof is not that explicit. Is there a way to construct the mixture distribution of the convolutional roots ? I mean a explicit mapping wich map's the mother mixture distribution and the "root size" to the new mixture distribution ?