= Solution
Use the standard global convention that $\mathcal M_c^2$ consists of <L2-bounded continuous martingales>, here starting at zero. This matters for arbitrary unbounded <stopping times> in part (iv); square-integrability at each separate deterministic time alone is weaker. Such <martingales> have terminal $L^2$ limits and satisfy the <optional sampling theorem> at arbitrary finite <stopping times>. Infinite <stopping times> can also be included by evaluating at the terminal limit. The <weakly orthogonal continuous martingales> condition compares cross-time <expectations>. The following four parts prove its equivalence with the equal-time, bracket-mean and forward-stopping tests.
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