10 Given the set $\Omega=\left\{(x, y) \mid x^{2}+y^{2} \leqslant 2008\right\}$, if points $P(x, y)$ and $P^{\prime}\left(x^{\prime}\right.$, $y^{\prime}$ ) satisfy $x \leqslant x^{\prime}$ and $y \geqslant y^{\prime}$, then point $P$ is said to dominate $P^{\prime}$. If a point $Q$ in set $\Omega$ satisfies: there does not exist any other point in $\Omega$ that dominates $Q$, then the set of all such points $Q$ is
10 is superior to $P^{\prime}$, i.e., $P$ is located to the left and above $P^{\prime}$, “there does not exist any point in $\Omega$ that is superior to $Q$”, i.e., “there is no point in $\Omega$ in the left and upper region of point $Q$”. Therefore, the set of points that satisfy the conditions is
$$
\left\{(x, y) \mid x^{2}+y^{2}=2008, x \leqslant 0, y \geqslant 0\right\} .
$$