Let (left(u_{n}, mathscr{A}_{n}ight)_{n in mathbb{N}}) be a martingale with (u_{n} in mathcal{L}^{2}left(mathscr{A}_{n}ight)). Show that [int u_{n} u_{k}

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Let \(\left(u_{n}, \mathscr{A}_{n}ight)_{n \in \mathbb{N}}\) be a martingale with \(u_{n} \in \mathcal{L}^{2}\left(\mathscr{A}_{n}ight)\). Show that

\[\int u_{n} u_{k} d \mu=\int u_{n \wedge k}^{2} d \mu\]

[ assume that \(n

Equation 23.1

-=_ p "n" [=1p1+"n"

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