A D992: Function $\upsilon : \mathcal{P}(X) \to [0, \infty]$ is an outer measure on $X$ if and only if
| Condition | Comment | |
| (1) | \begin{equation} \upsilon(\emptyset) = 0 \end{equation} | Preserves order-zero from $(\mathcal{P}(X), \subseteq)$ to $([0, \infty], {\leq})$ |
| (2) | \begin{equation} \forall \, E, F \in \mathcal{P}(X) \left( E \subseteq F \quad \implies \quad \upsilon(E) \leq \upsilon(F) \right) \end{equation} | ("D5371: Standard-isotone basic function") |
| (3) | \begin{equation} \forall \, E_0, E_1, E_2, \dots \in \mathcal{P}(X) : \upsilon \left( \bigcup_{n \in \mathbb{N}} E_n \right) \leq \sum_{n \in \mathbb{N}} \upsilon(E_n) \end{equation} | Countably subadditive function from $(\mathcal{P}(X), \cup, \cap)$ to $([0, \infty], +, \times)$ |