In mathematics – specifically, in stochastic analysis – Doob's martingale convergence theorems are a collection of results on the long-time limits of supermartingales, named after the American mathematician Joseph Leo Doob.
Read more about Doob's Martingale Convergence Theorems: Statement of The Theorems, Discrete-time Results, Convergence of Conditional Expectations: Lévy's Zero–one Law