Integral energy characterization of Hajłasz-Sobolev spaces

We provide an integral energy characterization of Hajłasz-Sobolev spaces M1,p(X,E) with p>1, where X is a metric measure space that satisfies weak Poincaré inequality and E is a Banach space with the Radon-Nikodym property. This result extends previously known results, which were originally established on Rn.