ThmDex – An index of mathematical definitions, results, and conjectures.
Triangle inequality for signed basic integral
Formulation 0
Let $M = (X, \mathcal{F}, \mu)$ be a D1158: Measure space such that
(i) $f : X \to [-\infty, \infty]$ is an D1921: Absolutely integrable function on $M$
Then \begin{equation} \int_X f \, d \mu \leq \left| \int_X f \, d \mu \right| \leq \int_X |f| \, d \mu \end{equation}