Absolutely Continuous Measures

Definitions

Let $(X,{\mathcal {M}},\mu _{1})$ be a measure space. The measure $\mu _{2}:{\mathcal {M}}\rightarrow [0,\infty ]$ is said to be absolutely continuous with respect to the measure $\mu _{1}$ if we have that $\mu _{1}(T)=0\implies \mu _{2}(T)=0$ where $T\in {\mathcal {M}}$.

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