Definition: A sequence of random variables $\x_n$ is bounded in probability if for any $\eps > 0$, there exist $M$ and $N$ such that $\Pr\lbrace\norm{\x_n} > M\rbrace < \eps$ for all $n > N$.
Definition: A sequence of random variables $\x_n$ is bounded in probability if for any $\eps > 0$, there exist $M$ and $N$ such that $\Pr\lbrace\norm{\x_n} > M\rbrace < \eps$ for all $n > N$.