Triangle Inequality for Integrals

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

Let $f: X \to \overline{\R}$ be a $\mu$-integrable function.

Then:


 * $\displaystyle \left\vert{\int f \, \mathrm d \mu}\right\vert \le \int \left\vert{f}\right\vert \, \mathrm d \mu$