ThmDex – An index of mathematical definitions, results, and conjectures.
Formulation F3880 on D1748: Signed basic integral
F3880
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 $M$
The signed integral of $f$ with respect to $M$ is the D993: Real number \begin{equation} \int_X f \, d \mu := \int_X f^+ \, d \mu - \int_X f^- \, d \mu \end{equation}