Ratner's measure classification theorem

Type: Concept

As of November 2026, Ratner's measure classification theorem has been mentioned in one podcast episode on Institute for Advanced Study (Jan 2026). Central theorem discussed in the podcast, classifying invariant measures in homogeneous spaces.

In mathematics, Ratner's theorems are a group of major theorems in ergodic theory concerning unipotent flows on homogeneous spaces proved by Marina Ratner around 1990. The theorems grew out of Ratner's earlier work on horocycle flows. The study of the dynamics of unipotent flows played a decisive role in the proof of the Oppenheim conjecture by Grigory Margulis. Ratner's theorems have guided key advances in the understanding of the dynamics of unipotent flows. Their later generalizations provide