Prove that: A right-continuous process $X$ adapted to the filtration $\{\mathcal{F}_t\}$ is a martingale if and only if for any bounded stopping time $T$, $X_T \in L^1$ and $E[X_T] = E[X_0]$.
I know the "only if" part, but how comes the "if" part?
2026-03-29 02:45:23.1774752323
About Martingale Stopping Theorem
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