Two measures are said to be singular w.r.t. each other if they are supported on disjoint sets.
Often "singular measure" means a measure that is singular with respect to Lebesgue measure (or Hausdorff measure).
Lebesgue's decomposition theorem, given two measures $\mu$, $\nu$, decomposes $\nu$ in two parts, one absolutely continuous with respect to $\mu$, and the other singular to it.
