  In this note we give new proofs of rectifiability of RCD(K,N) spaces as
metric measure spaces and lower semicontinuity of the essential dimension, via
$\delta$-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.
