  We explore the interplay between random and deterministic phenomena using a
representation of uncertainty based on the measure-theoretic concept of outer
measure. The meaning of the analogues of different probabilistic concepts is
investigated and examples of application are given. The novelty of this article
lies mainly in the suitability of the tools introduced for jointly representing
random and deterministic uncertainty. These tools are shown to yield intuitive
results in simple situations and to generalise easily to more complex cases.
Connections with Dempster-Shafer theory, the empirical Bayes methods and
generalised Bayesian inference are also highlighted.
