The collection of Lebesgue measurable subsets of $\mathbb{R}^n$ is a $\sigma$-algebra containing all open subsets of $\mathbb{R}^n$. The measure $\mathcal{L}^n$ is countably additive on this $\sigma$-algebra. If $(E_k)_{k=1}^\infty$ are pairwise disjoint Lebesgue measurable sets, then \begin{align*} \mathcal{L}^n\left(\bigcup_{k=1}^\infty E_k\right) = \sum_{k=1}^\infty \mathcal{L}^n(E_k). \end{align*} Moreover, $\mathcal{L}^n(\varnothing)=0$ and $\mathcal{L}^n(E) \le \mathcal{L}^n(F)$ whenever $E \subset F$ are Lebesgue measurable.