Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 327 / 3 / b / Solution

For a locally integrable $u$, the change of variables formula $y=Ax$ givesThis motivatesBecause pullback by an invertible linear map acts continuously on the Schwartz space, the right side is a continuous linear functional of $\phi$. It therefore defines a tempered distribution and agrees with ordinary pullback when $u$ is a function.