Definition 16.2.1. Let $(X, \cm)$ be a measure space, then
\[\mathcal{L}^{+}(X, \cm) = \bracs{f: X \to \real| f \ge 0, f \text{ is } (\cm, \cb_\real) \text{-measurable}}\]
is the space of non-negative $\real$-valued measurable functions on $(X, \cm)$.