Atom (measure theory)

In mathematics, more precisely in measure theory, an atom is a measurable set which has positive measure and contains no set of smaller positive measure. A measure which has no atoms is called non-atomic or atomless.

Given a measurable space ${\displaystyle (X,\Sigma )}$ and a measure ${\displaystyle \mu }$ on that space, a set ${\displaystyle A\subset X}$ in ${\displaystyle \Sigma }$ is called an atom if

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