  A Boolean algebra $\A$ equipped with a (finitely-additive) positive
probability measure $m$ can be turned into a metric space $(\A , d_{m})$, where
$d_{m}(a,b)= m ((a\wedge\neg b)\vee(\neg a\wedge b))$, for any $a,b\in A$,
sometimes referred to as \emph{metric Boolean algebra}. In this paper, we study
under which conditions the space of atoms of a finite metric Boolean algebra
can be isometrically embedded in $\mathbb{R}^{N}$ (for a certain $N$) equipped
with the Euclidean metric. In particular, we characterize the topology of the
positive measures over a finite algebra $\A$ such that the metric space
$(\mathsf{At}(\A), d_m)$ embeds isometrically in $\mathbb{R}^{N}$.
