Measurable dynamics has traditionally referred to ergodic theory, which is in some sense a sister topic to dynamical systems and chaos theory. However, the topic has until recently been a highly theoretical mathematical topic which is generally less obvious to those practitioners in applied areas, who may not find obvious links to practical, real-world problems. During the past decade, facilitated by the advent of high-speed computers, it has become practical to represent the notion of a transfer operator discretely but to high resolution thanks to rapidly developing algorithms and new numerical methods designed for the purpose. An early book on this general topic is Cell-to-Cell Mapping: A Method of Global Analysis for Nonlinear Systems [167] from 1987. A tremendous amount of progress and sophistication has come to the empirical perspective since then.