  There are two primary goals to this paper. In the first part of the paper we
study smooth metric measure spaces (M^n,g,e^{-f}dv_g) and give several ways of
characterizing bounds -Kg\leq \Ric+\nabla^2f\leq Kg on the Ricci curvature of
the manifold. In particular, we see how bounded Ricci curvature on M controls
the analysis of path space P(M) in a manner analogous to how lower Ricci
curvature controls the analysis on M. In the second part of the paper we
develop the analytic tools needed to in order to use these new
characterizations to give a definition of bounded Ricci curvature on general
metric measure spaces (X,d,m). We show that on such spaces many of the
properties of smooth spaces with bounded Ricci curvature continue to hold on
metric-measure spaces with bounded Ricci curvature.
