Martingale convergence theorem (source code)

= Martingale convergence theorem
{c}
{wiki=Doob's_martingale_convergence_theorems}

A discrete-time martingale with $\sup_n\mathbb E|M_n|<\infty$ converges almost surely to an integrable random variable. If the martingale is <uniform integrability>[uniformly integrable], convergence also holds in $L^1$.