Measuring the probabilistic powerdomain

In this paper we initiate the study of measurements on the probabilistic powerdomain. We show how measurements on the underlying domain naturally extend to the probabilistic powerdomain, so that the kernel of the extension consists of exactly those normalized valuations on the kernel of the measurement on the underlying domain. This result is combined with now-standard results from the theory of measurements to obtain a new proof that the fixed point associated with a weakly hyperbolic IFS with probabilities is the unique invariant measure whose support is the attractor of the underlying IFS