Let (left{X_{n}ight}_{n=1}^{infty}) be a sequence of random variables. Suppose that for every (varepsilon>0) we have that [limsup

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Let \(\left\{X_{n}ight\}_{n=1}^{\infty}\) be a sequence of random variables. Suppose that for every \(\varepsilon>0\) we have that

\[\limsup _{n ightarrow \infty} P\left(\left|X_{n}ight|>\varepsilonight) \leq c \varepsilon\]

where \(c\) is a finite real constant. Prove that \(X_{n} \xrightarrow{p} 0\) as \(n ightarrow \infty\).

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