Here's some interesting reading about a more rigorous treatment of the Dirac delta: https://en.m.wikipedia.org/wiki/Dirac_delta_function#As_a_distribution https

Here's some interesting reading about a more rigorous treatment of the Dirac delta: https://en.m.wikipedia.org/wiki/Dirac_delta_function#As_a_distribution https://en.m.wikipedia.org/wiki/Dirac_delta_function#As_a_di...