Let $X$ be a smooth variety, $\xi$ be a point of $X$ and $\mathfrak{a}$ be an ideal sheaf. If we define $mult_{\xi} \mathfrak{a}$ to be the largest integer $p$ such that $\mathfrak{a} \cdot \mathcal{O}_{X,\xi}\subseteq \mathfrak{m}_{\xi}^{p}$, where $\mathfrak{m}_{\xi}$ is the maximal ideal of $\mathcal{O}_{X,\xi}$, we have the map $\xi \mapsto mult_{\xi}\mathfrak{a}$.

Is this map upper-semicontinuous?