Suppose that (left{X_{n}ight}_{n=1}^{infty}) is a sequence of random variables such that (X_{n} xrightarrow{r} X) as (n ightarrow

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Suppose that \(\left\{X_{n}ight\}_{n=1}^{\infty}\) is a sequence of random variables such that \(X_{n} \xrightarrow{r} X\) as \(n ightarrow \infty\) for some random variable \(X\). Prove that for \(r>1\) that

\[\lim _{n ightarrow \infty} E\left(\left|X_{n}ight|^{r}ight)=E\left(|X|^{r}ight) .\]

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