I asked ChatGPT Legacy: "Hello! Can you prove how a martingale converges to the zariski measure on a commutative scheme?" It replied: "Hello! The notion of a

I asked ChatGPT Legacy: "Hello! Can you prove how a martingale converges to the zariski measure on a commutative scheme?" It replied: "Hello! The notion of a martingale converging to the Zariski measure on a commutative scheme is a highly advanced and abstract mathematical concept. It is not possible to provide a simple proof for this statement, as it requires a deep understanding of several advanced mathematical concepts such as probability theory, algebraic geometry, and commutative algebra." It then listed definitions for martingale, Zariski measure, and a commutative scheme, and then concluded with: "However, to fully understand this concept, you would need to study advanced mathematical topics such as algebraic geometry, commutative algebra, and probability theory." That seems like a useful enough answer with definitions that effectively converges to "I don't know."