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Unsigned basic measure
Unsigned basic integral measure
Formulation 0
Let $M = (X, \mathcal{F}, \mu)$ be a
D1158: Measure space
such that
(i)
$f : X \to [0, \infty]$ is a
D313: Measurable function
on $M$
The
unsigned basic integral measure
on $M$ with respect to $f$ is the
D4361: Unsigned basic function
\begin{equation} \mathcal{F} \to [0, \infty], \quad E \mapsto \int_E f \, d \mu \end{equation}
Child definitions
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D2888: Radon-Nikodym derivative