Paper detail

Gamma-convergence of Cheeger energies with respect to increasing distances

We prove a $Γ$-convergence result for Cheeger energies along sequences of metric measure spaces, where the measure space is kept fixed, while distances are monotonically converging from below to the limit one. As a consequence, we show that the infinitesimal Hilbertianity condition is stable under this kind of convergence of metric measure spaces.