Integration is Non-Decreasing

Last updated Nov 1, 2022

Let $(X, \mathcal{M}, \mu)$ be a Measure Space and let $f,g: X \to \mathbb{R}$ be Borel Measureable Functions so that $f \leq g$ $\mu$-Almost Everywhere. Then $$\int\limits_{X} f d \mu \leq \int\limits_{X} g d \mu$$

• Real Numbers
• Integration
• Non-Decreasing Function