Let $(X,\Sigma)$ be a measurable space and let $\mu$ and $\nu$ both be measures on $(X,\Sigma)$. Then $\mu$ and $\nu$ are singular, written $\mu \perp \nu$, if there exist disjoint sets $A,B\subset X$ such that $\mu \equiv 0$ outside of $A$ and $\nu \equiv 0$ outside of $B$. That is, $\mu(A’) = 0$ for all $A’\subset X\setminus A$ and $\nu(B’) =0$ for all $B’\subset X\setminus B$.
Wikidata ID: Q1824450