Measure

Definition

A measure on $X$ is a function $\mu :M\to [0,\infty ]$ such that:

1. $\mu (\varnothing )=0$
2. $\mu ({\cup }_{n=1}^{\infty }{A}_n)={\Sigma }_{n=1}^{\infty }\mu (A_n)$ (for pairwise disjoint $A_n\in M$)
   Then we say $X$ is a measure space.