Let ( X , M , μ 1 ) {\displaystyle (X,{\mathcal {M}},\mu _{1})} be a measure space. The measure μ 2 : M → [ 0 , ∞ ] {\displaystyle \mu _{2}:{\mathcal {M}}\rightarrow [0,\infty ]} is said to be absolutely continuous with respect to the measure μ 1 {\displaystyle \mu _{1}} if we have that μ 1 ( T ) = 0 ⟹ μ 2 ( T ) = 0 {\displaystyle \mu _{1}(T)=0\implies \mu _{2}(T)=0} where T ∈ M {\displaystyle T\in {\mathcal {M}}} .
![{\displaystyle \mu _{2}:{\mathcal {M}}\rightarrow [0,\infty ]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/98db72c9313a5f1a8af79396881782bea9858b9d)
