TY - RPRT T1 - The splitting theorem in non-smooth context Y1 - 2013 A1 - Nicola Gigli AB - 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. UR - http://preprints.sissa.it/handle/1963/35306 U1 - 35613 U2 - Mathematics U4 - 1 U5 - MAT/05 ER -