ThmDex – An index of mathematical definitions, results, and conjectures.
Signed basic integral of almost everywhere equal functions
Formulation 1
Let $M = (X, \mathcal{F}, \mu)$ be a D1158: Measure space such that
(i) $f, g : X \to [-\infty, \infty]$ are each an D1921: Absolutely integrable function on $M$
(ii) \begin{equation} f \overset{a.e.}{=} g \end{equation}
Then \begin{equation} \int_X f \, d \mu = \int_X g \, d \mu \end{equation}