Abstract
We establish a link between the distribution of an exponential functional, I, and the undershoots of a subordinator, which is given in terms of the associated harmonic potential measure. This allows us to give a necessary and sufficient condition in terms of the Levy measure for the exponential functional to be multiplicative infinitely divisible. We then provide a formula for the moment generating functions of log I and log R where R is the so-called remainder random variable associated to I. We provide a realization of the remainder random variable R as an infinite product involving independent last position random variables of the subordinator. Some properties of harmonic measures are obtained and some examples are provided.