Solution
= Solution
Bilinearity and symmetry are immediate. Since $r\geq0$, $\langle u,u\rangle\geq0$. If this is zero, continuity of $u^2r$ makes it identically zero. The points where $r>0$ are dense because only finitely many are excluded, so $u$ vanishes on a dense set and hence everywhere. Thus the form is an <inner product>.