Definition:Atom of Measure

Definition
Let $\left({X, \Sigma, \mu}\right)$ be a measure space.

An element $x \in X$ is said to be an atom (of $\mu$) iff:


 * $(1):\quad \left\{{x}\right\} \in \Sigma$
 * $(2):\quad \mu \left({\left\{{x}\right\}}\right) > 0$

Also see

 * Diffuse measures are measures without atoms