Completion (7). Let (left(u_{n}, mathscr{A}_{n}ight)_{n in mathbb{N}}) be a submartingale and denote by (overline{mathscr{A}}_{n}) the completion of

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Completion (7). Let \(\left(u_{n}, \mathscr{A}_{n}ight)_{n \in \mathbb{N}}\) be a submartingale and denote by \(\overline{\mathscr{A}}_{n}\) the completion of \(\mathscr{A}_{n}\). Then \(\left(u_{n}, \overline{\mathscr{A}}_{n}ight)_{n \in \mathbb{N}}\) is still a submartingale.

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