Exercise 13, § 1

Let $F$ be a Hausdorff locally convex space, $F'$ its dual, $q$ a lower semi-continuous semi-norm on $F$. Show that if $f$ is a mapping of $T$ into $F$, $\mu$-measurable for the topology $\sigma(F,F')$, then the numerical function $q \circ f$ is $\mu$-measurable.

EXERCISES