I have read an econometrics textbook on "converge in distribution" and found the following sentence.
\begin{equation} \text{If} \hspace{0.25 cm} Z_{N} \xrightarrow{d} Z, Z_{N} = \large{O_p}(1)
\end{equation}That is, if a random variable $Z_n$ converges in distribution to $Z$, $Z_N$ is bounded in probability.
The textbook states that this is easy to verify. However, I cannot figure it out at the moment. thus, could you please help me prove the statement above?
Your helps are highly appreciated and Thank you very much.
