Uniformly integrable martingale convergence theorem
= Uniformly integrable martingale convergence theorem
A <uniformly integrable> <martingale> $M_n$ has <almost sure convergence> and <convergence in L1> to an <integrable random variable> $M_\infty$, and $M_n=\mathbb E[M_\infty\mid\mathcal F_n]$.