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Complete measure
Formulation 0
A D85: Unsigned basic measure $\mu : \mathcal{F} \to [0, \infty]$ is complete if and only if \begin{equation} \forall \, F \in \mathcal{F} \left( \mu(F) = 0 \quad \implies \quad \forall \, E \subseteq F : E \in \mathcal{F} \right) \end{equation}
Formulation 1
Let $M = (X, \mathcal{F}, \mu)$ be D1158: Measure space such that
(i) $\mathsf{Subnull} = \mathsf{Subnull}(M)$ is the D3804: Set of subnull sets in $M$
Then $\mu$ is a complete measure if and only if \begin{equation} \mathsf{Subnull} \subseteq \mathcal{F} \end{equation}
Child definitions
» D1678: Complete measure space
» D3774: Complete probability measure