# Does $|X_n|\le\Delta_n+\delta$, with $\Delta_n\overset{p}\to0$ imply $|X_n|\overset{p}\to0$?

by J.Mike   Last Updated May 15, 2019 18:20 PM

Suppose $$\Delta_n\overset{p}\to0$$, and for any $$\delta>0$$, we have $$|X_n|\le\Delta_n+\delta.$$

Can we conclude that

$$|X_n|\overset{p}\to0?$$

Here $$\Delta_n\overset{p}\to0$$ means that for any $$\varepsilon>0$$, we have $$\lim_{n\to\infty}P(|\Delta_n|>\varepsilon)=0$$.

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