Let ((X, mathscr{A}, mu)) be a measure space and (left(u_{n}ight)_{n in mathbb{N}} subset L^{1}(mathscr{A})). Show that [m_{1}:=u_{1},
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Let \((X, \mathscr{A}, \mu)\) be a measure space and \(\left(u_{n}ight)_{n \in \mathbb{N}} \subset L^{1}(\mathscr{A})\). Show that
\[m_{1}:=u_{1}, \quad m_{n+1}-m_{n}:=u_{n+1}-\mathbb{E}^{\mathscr{A}_{n}} u_{n+1}\]
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