 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-3/26l/c/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

Yes. The

L^{2}

bound makes the family uniformly integrable in

L^{1}

E [∣ X_{n} ∣ 1_{∣ X_{n} ∣ > K}] \leq E [X_{n}^{2}] / K \leq 1/ K

E ∣ X_{n} ∣ \to 0

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