Definition:Atom of Sigma-Algebra

Sets
Let $\left({X, \Sigma}\right)$ be a measurable space.

Let $E \in \Sigma$ be nonempty.

$E$ is said to be an atom (of $\Sigma$) iff it satisfies:


 * $\forall F \in \Sigma: F \subsetneq E \implies F = \varnothing$

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

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


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