  Domain theory has a long history of applications in theoretical computer
science and mathematics. In this article, we explore the relation of domain
theory to probability theory and stochastic processes. The goal is to establish
a theory in which Polish spaces are replaced by domains, and measurable maps
are replaced by Scott-continuous functions. We illustrate the approach by
recasting one of the fundamental results of stochastic process theory --
Skorohod's Representation Theorem -- in domain-theoretic terms. We anticipate
the domain-theoretic version of results like Skorohod's Theorem will improve
our understanding of probabilistic choice in computational models, and help
devise models of probabilistic programming, with its focus on programming
languages that support sampling from distributions where the results are
applied to Bayesian reasoning.
