The map $\lambda^{*}:\mathcal{P}(X)\to \mathbb{R}^{+}\cup\{\infty\}$ is an outer measure if: 1. $\lambda^{*}(\emptyset)=0$ 2. Monotonicity: $A\subset B\implies\lambda^{*}(A)\le\lambda^{*}(B)$ 3. Countable Subadditivity: $$A_{1},A_{2},\dots\in\mathcal{P}(X)\implies\lambda^{*}\left( \bigcup_{n=1}^\infty A_{n} \right)\le\sum_{n=1}^{\infty}\lambda^{*}(A_{n})$$