Solution
= Solution
The <restriction of a measure to a measurable subset> is $(\mu|_M)(A)=\mu(A\cap M)$ for every measurable $A$. <Absolute continuity of measures>, written $\mu\ll\kappa$, means $\kappa(A)=0\implies\mu(A)=0$. The <measures> are <mutually singular> when a measurable $S$ satisfies $\kappa(S)=0$ and $\mu(X\setminus S)=0$. Thus singularity means concentration on a <null set> of the other <measure>; it does not assert that every <measurable set> is null for one of them.