ThmDex – An index of mathematical definitions, results, and conjectures.
Isotonicity of unsigned basic integral
Formulation 2
Let $M = (X, \mathcal{F}, \mu)$ be a D1158: Measure space such that
(i) $f, g : X \to [0, \infty]$ are each an D5610: Unsigned basic Borel function on $M$
(ii) \begin{equation} f \overset{a.e.}{\leq} g \end{equation}
Then \begin{equation} \int_X f \, d \mu \leq \int_X g \, d \mu \end{equation}