Explore lossy compression techniques for data supported on general structures in this 44-minute talk. Delve into rate-distortion theory and quantization of random variables in measurable spaces like manifolds and fractal sets. Examine the prevalence of manifold structures in data science applications and the use of fractal sets in image compression and Ethernet traffic modeling. Discover bounds on the rate-distortion function and quantization error, applicable to various scenarios with minimal requirements. Apply these concepts to specific examples, including hyperspheres, Grassmannians, and self-similar sets characterized by iterated function systems. Gain insights into the wide-ranging implications of these compression techniques across different fields of study.