  We consider the Rademacher- and Sobolev-to-Lipschitz-type properties for
arbitrary quasi-regular strongly local Dirichlet spaces. We discuss the
persistence of these properties under localization, globalization, transfer to
weighted spaces, tensorization, and direct integration. As byproducts we
obtain: necessary and sufficient conditions to identify a quasi-regular
strongly local Dirichlet form on an extended metric topological $\sigma$-finite
possibly non-Radon measure space with the Cheeger energy of the space; the
tensorization of intrinsic distances; the tensorization of the Varadhan
short-time asymptotics.
