# Definition
A **measure** on $X$ is a function $\mu : M \to [0,\infty]$ such that:
1. $\mu(\emptyset) = 0$
2. $\mu(\cup^{\infty}_{n=1}A_{n}) = \Sigma^{\infty}_{n=1} \mu(A_{n})$ (for pairwise disjoint $A_{n} \in M$)
Then we say $X$ is a measure space.