= Finite-bracket convergence lemma
{title2=$\langle M\rangle_\infty<\infty\ \Longrightarrow\ M_t\text{ converges finitely}$}
A continuous local martingale converges to a finite limit on the event that its terminal bracket is finite. Stopping at each integer bracket level gives an L2-bounded martingale and its almost sure limit. On the finite-bracket event, some such stopped process coincides with the original process forever. This supplies terminal values for a finite DDS lifetime.
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