Absolutely Continuous Measures

Definitions

Let $(X,{\mathcal {M}},\mu _{1})$ be a measure space. The measure $\mu _{2}$ is said to be absolutely continuous with respect to $\mu _{1}$ if $\mu _{1}(T)=0\implies \mu _{2}(T)=0$ where $T\in {\mathcal {M}}$.