Hajlasz Gradients Are Upper Gradients

Renjin Jiang, Nageswari Shanmugalingam, Dachun Yang +1

Let $(X,d,\mu )$ be a metric measure space, with $\mu$ a Borel regular measure. In this paper, we prove that, if $u\in L_{\mathrm{loc}}^1(X)$ and $g$ is a Hajłasz gradient…