  The main result of this article states that the (K;N)-cone over some metric
measure space satisfies the reduced Riemannian curvature-dimension condition
RCD^*(KN;N+1) if and only if the underlying space satisfies RCD^*(N-1;N). The
proof uses a characterization of reduced Riemannian curvature-dimension bounds
by Bochner's inequality that was established for metric measure spaces by
Erbar, Kuwada and Sturm and independently by Ambrosio, Mondino and Savar\'e. As
corollary of our result and the Cheeger-Gigli-Gromoll splitting theorem we
obtain a maximal diameter theorem for metric measure spaces that satisfy a
reduced Riemannian curvature-dimension condition.
