Exercise 4, § 5

a) Let $\mu$ be a moderated measure $\geq 0$ on T. Show that there exists a function $h \geq 0$, continuous on T, such that $h \cdot \mu$ is bounded and is equivalent to $\mu$ (argue as for Prop. 11). b) Let $(\mu_n)$ be a sequence of moderated measures $\geq 0$ on T. Show that there exists a measure $\mu \geq 0$ on T such that each $\mu_n$ has base $\mu$ (reduce to the case that each of the $\mu_n$ is bounded).