Definition:Atom of Sigma-Algebra

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

Let $E \in \Sigma$ be nonempty.

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


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

Thus, atoms are the minimal non-empty sets in $\Sigma$ with respect to the subset ordering.