Exercise 1, § 2

Let X be a locally compact space, $\Phi$ a filter on $\mathscr{M}(X; \mathbf{C})$ such that the support of $\mu$ recedes indefinitely along $\Phi$ (No. 2, preceding Prop. 7); show that for the quasi-strong topology (§1, Exer. 8), $\mu$ tends to 0 with respect to $\Phi$.