ACIT4330-Page/content/Definitions/Measure Theory/Lebesgue Integral.md

The Lebesgue Integral (over A \in M) of Measurable f : X \to [0, \infty] is \int_{A} f \, d\mu \equiv \underbrace{\sup_{0 \leq s \leq f}}_{s\ \text{measurable and simple}} \int_{A} s \, d\mu \in [0, \infty].