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The aim of the present paper is to bridge the gap between the Bakry-\'{E}meryand the Lott-Sturm-Villani approaches to provide synthetic and abstract notionsof lower Ricci curvature bounds. We start from a strongly local Dirichlet form${{\mathcal{E}}}$ admitting a Carr\'{e} du champ $\Gamma$ in a Polish measurespace $(X,\mathfrak{m})$ and a canonical distance${\mathsf{d}}_{{{\mathcal{E}}}}$ that induces the original topology of $X$. Wefirst characterize the distinguished class of Riemannian Energy measure spaces,where ${\mathcal{E}}$ coincides with the Cheeger energy induced by${\mathsf{d}}_{{\mathcal{E}}}$ and where every function $f$ with$\Gamma(f)\le1$ admits a continuous representative. In such a class, we showthat if ${{\mathcal{E}}}$ satisfies a suitable weak form of the Bakry-\'{E}merycurvature dimension condition $\mathrm {BE}(K,\infty)$ then the metric measurespace $(X,{\mathsf{d}},\mathfrak{m})$ satisfies the Riemannian Ricci curvaturebound $\mathrm {RCD}(K,\infty)$ according to [Duke Math. J. 163 (2014)1405-1490], thus showing the equivalence of the two notions. Two applicationsare then proved: the tensorization property for Riemannian Energy spacessatisfying the Bakry-\'{E}mery $\mathrm {BE}(K,N)$ condition (and thus thecorresponding one for $\mathrm {RCD}(K,\infty)$ spaces without assumingnonbranching) and the stability of $\mathrm {BE}(K,N)$ with respect toSturm-Gromov-Hausdorff convergence.

Bakry-\'Emery curvature-dimension condition and Riemannian Ricci curvature bounds