Let $A$ be a unital abelian complex von Neumann algebra, with atomicity meaning that every nonzero projection in $A$ dominates a nonzero minimal projection in $A$. Then $A$ is atomic if and only if there exists a set $I$ and a unital normal $*$-isomorphism
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\begin{align*}
A \cong \ell^\infty(I)
\end{align*}
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where $\ell^\infty(I)$ is the von Neumann algebra of bounded complex-valued functions on $I$ with pointwise operations and the supremum norm.