Oscillating point-mass defect
= Oscillating point-mass defect
{title2=$u_j=v+c_j\delta_p+o_{\mathcal D'}(1)$}
A sequence can converge as <distributions> off one point while retaining a nonconvergent multiple of a <Dirac delta function> at that point. If $u_j=v+c_j\delta_p+o_{\mathcal D'}(1)$ with $c_j$ nonconvergent, restriction to the punctured domain tends to $v$, but a test nonzero at $p$ detects the obstruction to global convergence.