Normalizable

A function $f$ on a Metric space $(X,\Vert \cdot \Vert )$ is normalizable iff $\Vert f\Vert \in {\mathbb{R}}^{+}$.

This property is often required of the Quantum state of a system, in order for it to have physical meaning, which means $\Vert \psi {\Vert }_{L_2}={\int }_{\mathbb{R}}|\psi (x){|}^{2}dx\in {\mathbb{R}}^{+}$, where $L_2$ is the set of square-integrable functions.