Atom (measure theory)
= Atom
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= Atom of a measure
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An atom of a <measure> $\mu$ is a measurable set $A$ of positive measure for which every measurable $B\subseteq A$ has either $\mu(B)=0$ or $\mu(B)=\mu(A)$. A singleton of positive mass is an example. A <transport map> cannot split the mass of a singleton among several destinations.