Abstract
Domains arose as the first mathematical models for high-level programming languages. Over time, they have proven to be useful much more broadly, having found applications in mathematics, various areas of computer science, and beyond. Measure theory has played an important role for domains in modeling probabilistic computation. Conversely, domains have provided new insights into measure theory and especially, into probability theory and the theory of stochastic processes. The goal of this talk is to describe the relationship between these areas and how they have interacted. We’ll begin with a brief primer on domains and their basic features. We’ll then consider the traditional domain-theoretic approach to probability measures, namely as valuations. We’ll next describe how the domain-theoretic view of measures and the more traditional functional analytic approach are related. The remainder of the talk will be devoted to describing some of the applications of the domain-theoretic view of measures, including some recent results about domain theory and random variables.