Explore the concept of causal evolution of measures and the continuity equation in globally hyperbolic spacetimes through this 45-minute lecture by Tomasz Miller at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the mathematical framework of time-evolving probability measures on Cauchy hypersurfaces and discover three equivalent descriptions of causal time-evolution. Examine the use of probability measures on causal curves, causal L2_loc-vector fields, and the continuity equation to encapsulate causality in measure evolution. Investigate how these descriptions relate to each other and transform under changes in temporal functions. Gain insights into the extension of this formalism to N-particle causality theory and engage with topics such as nonlocal measures, causal curves, topology, and deparameterization.