  The aim of this paper is to establish a theory of random variables on
domains. Domain theory is a fundamental component of theoretical computer
science, providing mathematical models of computational processes. Random
variables are the mainstay of probability theory. Since computational models
increasingly involve probabilistic aspects, it's only natural to explore the
relationship between these two areas. Our main results show how to cast results
about random variables using a domain-theoretic approach. The pay-off is an
extension of the results from probability measures to sub-probability measures.
We also use our approach to extend the class of domains for which we can
classify the domain structure of the space of sub-probability measures.
