Limit of probabilities under equivalent measure

Question

I have a question. Let $\mathbb{P}$ and $\mathbb{Q}$ be equivalent measures, and let $A_n,n\in\mathbb{N}$ be a sequence of events on the regarding measure space. Does it hold true, that \begin{align} \lim\limits_{n\to\infty}\mathbb{P}(A_n)=0 \Rightarrow \lim\limits_{n\to\infty}\mathbb{Q}(A_n)=0. \end{align}

Thank you very much.