Definition:Atom of Measure

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This page is about atoms of a measure. For other uses, see Definition:Atom.

Definition

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


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

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


Also see


Linguistic Note

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.


Sources