Integrable discrete-time local martingale is a martingale
= Integrable discrete-time local martingale is a martingale
An integrable discrete-time <local martingale> is a true <martingale>. Its stopped increments have the form $\mathbf1_{\{\tau\geq t\}}(X_t-X_{t-1})$, and the <dominated convergence theorem> removes a <localizing sequence> from the conditional increment identity.