4. Given the ellipse $C: \frac{x^{2}}{2}+y^{2}=1$ with two foci $F_{1}$ and $F_{2}$, point $P\left(x_{0}, y_{0}\right)$ satisfies $0<\frac{x_{0}^{2}}{2}+y_{0}^{2} \leqslant 1$. Then the range of $\left|P F_{1}\right|+\left|P F_{2}\right|$ is $\qquad$
4. $[2,2 \sqrt{2}]$.

From $0<\frac{x_{0}^{2}}{2}+y_{0}^{2} \leqslant 1$, we know that point $P\left(x_{0}, y_{0}\right)$ is inside the ellipse $C$ (including the boundary).
Therefore, $2 \leqslant\left|P F_{1}\right|+\left|P F_{2}\right| \leqslant 2 \sqrt{2}$.