MathGloss

Let $\mathcal P(X)$ be the power set of $X$. An outer measure on $X$ is a function $\mu: \mathcal P(X) \to [0,\infty]$ such that

• $\mu(\emptyset) = 0$
• if $A, B \subset X$ with $A\subset B$, then $\mu(A) \leq\mu(B)$
• for arbitrary subsets $B_i \subset X$ for $i \in \mathbb N$, we have $\mu\left(\bigcup\limits_{i\in\mathbb N} B_i \right)\leq \sum\limits_{i\in\mathbb N}\mu(B_i)$. Wikidata ID: Q258374

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