%0 Journal Article
%T On the Bakry-¨¦mery condition, the gradient estimates and the Local-to-Global property of RCD*(K,N) metric measure spaces
%A Luigi Ambrosio
%A Andrea Mondino
%A Giuseppe Savar¨¦
%J Mathematics
%D 2013
%I arXiv
%R 10.1007/s12220-014-9537-7.
%X We prove higher summability and regularity of \Gamma(f) for functions f in spaces satisfying the Bakry-\'Emery condition BE(K,\infty). As a byproduct, we obtain various equivalent weak formulations of BE(K,N) and we prove the Local-to-Global property of the RCD*(K,N) condition in locally compact metric measure spaces (X,d,m), without assuming a priori the non-branching condition on the metric space.
%U http://arxiv.org/abs/1309.4664v1