Rectifiability of the reduced boundary for sets of finite perimeter over $\RCD(K,N)$ spaces.

This note is devoted to the study of sets of finite perimeter over $\RCD(K,N)$ metric measure spaces. Its aim is to complete the picture about the generalization of De Giorgi's theorem within this framework. Starting from the results of \cite{ABS18} we obtain uniqueness of tangents and rectifiability for the reduced boundary of sets of finite perimeter. As an intermediate tool, of independent interest, we develop a Gauss-Green integration by parts formula tailored to this setting. These results are new and non-trivial even in the setting of Ricci limits.