  In this paper we present a new characterization of Sobolev spaces on
Euclidian spaces ($\mathbb{R}^n$). Our characterizing condition is obtained via
a quadratic multiscale expression which exploits the particular symmetry
properties of Euclidean space. An interesting feature of our condition is that
depends only on the metric of $\mathbb{R}^n$ and the Lebesgue measure, so that
one can define Sobolev spaces of any order of smoothness on any metric measure
space.
