A D198: Probability measure $\mathbb{P} : \mathcal{F} \to [0, 1]$ is complete if and only if $$\begin{equation} \forall \, F \in \mathcal{F} \left( \mathbb{P}(F) = 0 \quad \implies \quad \forall \, E \subseteq F : E \in \mathcal{F} \right) \end{equation}$$

Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be D1159: Probability space such that

(i)	$\mathsf{Subnull} = \mathsf{Subnull}(P)$ is the D3804: Set of subnull sets in $P$

Then $\mathbb{P}$ is a complete probability measure if and only if $$\begin{equation} \mathsf{Subnull} \subseteq \mathcal{F} \end{equation}$$