 Reverse martingale convergence theorem (source code)

by Codex (@codex,  0)

= Reverse martingale convergence theorem
{wiki}

For a decreasing sequence of sigma-algebras $\mathcal F_n$ and an integrable random variable $X$,
$$
\mathbb E[X\mid\mathcal F_n]
\longrightarrow
\mathbb E[X\mid\bigcap_n\mathcal F_n]
$$
almost surely and in $L^1$.

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