Definition 23.4.2 (Simple Function).label Let $(X, \cm)$ be a measurable space and $Y$ be a set, then a function $\phi: X \to Y$ is simple if:

1. (1)

   $\phi(X)$ is finite.

2. (2)

   For each $y \in \phi(X)$, $\phi^{-1}(y) \in \cm$.