singular measure

Two measures $\mu$ and $\nu$ in a measurable space $(\mathrm{\Omega },𝒜)$ arecalled singular if there exist two disjoint sets $A$ and $B$ in $𝒜$ such that $A\cup B=\mathrm{\Omega }$ and $\mu (B)=\nu (A)=0$.This is denoted by $\mu ⟂\nu$.