ABSTRACT
Measure theory provides a rigorous mathematical foundation for the study of, among other things, integration and probability theory. The study of stochastic processes, and of related control problems, can proceed some distance without reference to measure theoretic ideas. However, certain issues cannot be resolved fully without it, for example, the very existence of an optimal control in general models. In addition, if we wish to develop models which do not assume that all random quantities are stochastically independent, which we sooner or later must, the theory of martingale processes becomes indepensible, an understanding of which is greatly aided by a familiarity with measure theoretic ideas. Above all, foundational ideas of measure theory will be required for the function analytic construction of iterative algorithms.
