Definition:Atom of Sigma-Algebra

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

Let $A \in \mathcal A$ be nonempty.

$A$ is said to be an atom (of $\mathcal A$) iff it satisfies:


 * $\forall B \in \mathcal A: B \subsetneq A \implies B = \varnothing$

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

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


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