Consider on the measure space (left([0, infty), mathscr{B}[0, infty),left.lambda^{1}ight|_{[0, infty)}ight)) the filtration defined by (mathscr{A}_{n}:=sigma([0,1),[0,2), ldots,[n-1, n),[n,

Question:

Consider on the measure space $\left([0, \infty), \mathscr{B}[0, \infty),\left.\lambda^{1}ight|_{[0, \infty)}ight)$ the filtration defined by $\mathscr{A}_{n}:=\sigma([0,1),[0,2), \ldots,[n-1, n),[n, \infty))$. Find $\mathbb{E}^{\mathscr{A}_{n}} u$ for $u \in L^{p}$.

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