Definition 29.1.1 (Weakly Measurable).label Let $(X, \cm)$ be a measurable space, $E$ be a locally convex space over $K \in \RC$, and $f: X \to E$, then $f$ is weakly measurable if for each $\phi \in E^{*}$, $\phi \circ f: X \to K$ is Borel measurable.