ThmDex – An index of mathematical definitions, results, and conjectures.
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▼ Unsigned basic measure
Definition D3880
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}
Children
▶ D2888: Radon-Nikodym derivative