Category:Mutually Singular Measures

This category contains results about Mutually Singular Measures.
Definitions specific to this category can be found in Definitions/Mutually Singular Measures.

Let $\struct {X, \Sigma}$ be a measurable space.

Let $\mu$ be a measure, signed measure or complex measure on $\struct {X, \Sigma}$.

Let $\nu$ be a measure, signed measure or complex measure on $\struct {X, \Sigma}$.

We say that $\mu$ and $\nu$ are mutually singular if and only if there exists $E \in \Sigma$ such that:

$\mu$ is concentrated on $E$ and $\nu$ is concentrated on $E^c$.

We write:

$\mu \perp \nu$