Integral of Integrable Function is Monotone

Theorem
Let $\left({X, \Sigma, \mu}\right)$ be a measure space.

Let $f, g: X \to \overline{\R}$ be $\mu$-integrable functions.

Suppose that $f \le g$ pointwise.

Then:


 * $\displaystyle \int f \, \mathrm d \mu \le \int g \, \mathrm d \mu$