Explore the third installment of Andreas Bernig's lecture series on curvature tensors and measures of singular spaces, delivered as part of the Thematic Programme "Geometry beyond Riemann: Curvature and Rigidity" at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into advanced mathematical concepts and their applications in geometry over the course of this 55-minute talk, expanding your understanding of singular spaces and their curvature properties.