Let (left{X_{n}ight}_{n=1}^{infty}) be a sequence of random variables such that [Eleft(sup _{n in mathbb{N}}left|X_{n}ight|ight)

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Let \(\left\{X_{n}ight\}_{n=1}^{\infty}\) be a sequence of random variables such that

\[E\left(\sup _{n \in \mathbb{N}}\left|X_{n}ight|ight)<\infty\]

Prove that the sequence \(\left\{X_{n}ight\}_{n=1}^{\infty}\) is uniformly integrable.

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