Let $(X,\mathcal{F},\mu)$ be a measure space. This space is called σ-finite if $X$ can be written as the countable union of sets of finite Measure. i.e. $\exists A_{1},A_{2},\dots\in\mathcal{F}$ where $\mu(A_{i})<\infty$ such that: $$X=\bigcup_{n\in\mathbb{N}} A_{i}$$