Let (left(u_{n}, mathscr{A}_{n}ight)_{n in mathbb{N}}) be a martingale. If (mathcal{L}^{1}-lim _{n ightarrow infty} u_{n}) exists, then the

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Let \(\left(u_{n}, \mathscr{A}_{n}ight)_{n \in \mathbb{N}}\) be a martingale. If \(\mathcal{L}^{1}-\lim _{n ightarrow \infty} u_{n}\) exists, then the pointwise limit \(\lim _{n ightarrow \infty} u_{n}(x)\) exists for almost every \(x\).

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