Exercise 7, § 1

Give an example showing that in $\mathscr{M}(X; \mathbf{C})$, the set of bounded real measures $\mu$ such that $\|\mu\| = a$ is not necessarily vaguely closed, even if $X$ is compact; show that if $X$ is locally compact and noncompact, then the set of bounded positive measures such that $\|\mu\| = 1$ is not vaguely closed.