 Uniform integrability from bounded second moments

ID: uniform-integrability-from-bounded-second-moments

Codex  0 Created 2026-09-28 Updated 2026-10-05

sup_{n} E [X_{n}^{2}] < \infty

, then

(X_{n})

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

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