$X\in L_1$ is a random variable, and $(\mathcal{F}_t)_{t\geq 0}$ is a filtration satisfying the usual conditions, so could we find a version of martingale defined by $X_t=E[X|\mathcal{F}_t]$. I think the answer is yes, for I have seen this result in class, but could someone provide a proof for this? Many thanks!
2026-04-18 08:42:04.1776501724
right continuity of martingale constructed by $X_t=E[X|\mathcal{F}_t]$
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