ACIT4330-Page/content/Definitions/Measure Theory/Sigma-Algebra/Measure.md

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.