> [!definition] > > Let $(X, \cm)$ be a [[Sigma Algebra|measurable space]], $E$ be a [[Banach Space|Banach space]] over $F \in \bracs{\real, \complex}$, and $f: X \to E$ be a [[Function|function]], then $f$ is **weakly $\cm$-measurable** if for each $\phi \in E^*$, $\phi \circ f: X \to \complex$ is $(\cm, \cb(F))$-[[Measurable Function|measurable]].