  This paper establishes sufficient general conditions for the existence of
Mosco limits of Korevaar-Schoen $L^2$ energies, first in the context of Cheeger
spaces and then in the context of fractal-like spaces with walk dimension
greater than 2. Among the ingredients, a new Rellich-Kondrachov type theorem
for Korevaar-Schoen-Sobolev spaces is of independent interest.
