  It is a well known fact that, if $\Sigma$ is an Einstein hypersurface with
positive scalar curvature, then it is a round sphere. We give a stable version
of this result showing that if a hypersurface is almost Einstein in a
$L^p$-sense, then it is $W^{2, \, p}$ - close to the round sphere. The result
is given in a quantitative way.
