  A Radon measure $\mu$ is $n$-rectifiable if $\mu\ll\mathcal{H}^n$ and
$\mu$-almost all of $\text{supp}\,\mu$ can be covered by Lipschitz images of
$\mathbb{R}^n$. In this paper we give a necessary condition for rectifiability
in terms of the so-called $\alpha_2$ numbers -- coefficients quantifying
flatness using Wasserstein distance $W_2$. In a recent article we showed that
the same condition is also sufficient for rectifiability, and so we get a new
characterization of rectifiable measures.
