  We prove that an infinitesimally Hilbertian CD(0,N) space containing a line
splits as the product of $R$ and an infinitesimally Hilbertian CD(0,N-1) space.
By `infinitesimally Hilbertian' we mean that the Sobolev space
$W^{1,2}(X,d,m)$, which in general is a Banach space, is an Hilbert space. When
coupled with a curvature-dimension bound, this condition is known to be stable
with respect to measured Gromov-Hausdorff convergence.
