By <multiplication of a distribution by a smooth function>, for every <test function> $\psi$,
$$
\langle\rho\delta_0,\psi\rangle
=\langle\delta_0,\rho\psi\rangle
=\rho(0)\psi(0)=\psi(0)
=\langle\delta_0,\psi\rangle.
$$
Hence $\rho\delta_0=\delta_0$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 327 / 2 / b / i / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/iii/paper-327/2/b/i/solution