Let $(\Omega, \mathcal{F}, (\mathcal{F}_n)_{n\in\{0,1,2,\ldots,N\}}, P)$ be a stochastic basis, carrying an adapted and integrable stochastic process $X=X_n$. Show that X is a martingale iff $E[X_T]=E[X_S]$ for all bounded stopping times $S ≤T$.
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