Rectifiability of RCD(K,N) spaces via δ-splitting maps

. In this note we give simplified proofs of rectifiability of RCD( K, N ) spaces as metric measure spaces and lower semicontinuity of the essential dimension, via δ -splitting maps. The arguments are inspired by the Cheeger–Colding theory for Ricci limits and rely on the second order differential calculus developed by Gigli and on the convergence and stability results by Ambrosio– Honda