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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