Exercise 1, § 3

In $\mathbf{R}^2$, let $\lambda$ and $\mu$ be the positive measures

Show that $\lambda$ and $\mu$ are convolvable. Let $u$ be the homomorphism $(x, y) \mapsto x$ of $\mathbf{R}^2$ onto $\mathbf{R}$. Show that $u$ is $\lambda$-proper and $\mu$-proper, but that $u(\lambda)$ and $u(\mu)$ are not convolvable.