ThmDex – An index of mathematical definitions, results, and conjectures.
F10299
Formulation 0
Let $M = (X, \mathcal{F}, \mu)$ be a D1158: Measure space such that
(i) $f, g : X \to [-\infty, \infty]$ are each a D5566: Measurable basic function on $M$
(ii) \begin{equation} \Vert f \Vert_{L^1}, \Vert g \Vert_{L^1} < \infty \end{equation}
(iii) \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}