ACIT4330-Page/content/Definitions/Measure Theory/Lebesgue's Monotone Convergence Theorem.md

Definition

Say X has a Measure \mu, and let f_{n} : X \to [0, \infty] be Measurable and f_{1} \leq f_{2} \leq f_{3} \leq \dots.

Then \int f_{m} \, d\mu \to \int \lim_{ n \to \infty } f_{n} \, d\mu as m \to \infty.