00744nas a2200097   4500008004100000245004800041210004300089520044800132100001800580856004800598       2013                        en  d00aThe splitting theorem in non-smooth context0 asplitting theorem in nonsmooth context3 aWe 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.1 aGigli, Nicola  uhttp://preprints.sissa.it/handle/1963/35306