Definition:Atom of Measure

This page is about atoms in the context of measures. For other uses, see Atom.

Definition

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

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

$(1): \quad \set x \in \Sigma$

$(2): \quad \map \mu {\set x} > 0$

The word atom comes from the Greek ἄτομον, meaning unbreakable or indecomposable.

It is pronounced with a short a, as at-tom, as opposed to ay-tom.