Doob's martingale convergence theorems
= Doob's martingale convergence theorems
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These are convergence results for martingales and submartingales under appropriate one-sided or absolute-integrability bounds. They distinguish almost-sure convergence from convergence in mean: uniform integrability gives the latter. The <martingale convergence theorem> stated for an L1-bounded martingale is one standard member of the family.