Definition:Continuous Measure/At Point

Definition

Let $\struct {X, \Sigma}$ be a measurable space such that:

$\set x \in \Sigma$ for all $x \in X$.

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

Let $y \in X$.

We say that $\mu$ is continuous at $y$ if and only if:

$\map \mu {\set y} = 0$