  A domain is called Kac regular for a quadratic form on $L^2$ if the closure
of all functions vanishing almost everywhere outside a closed subset of the
domain coincides with the set of all functions vanishing almost everywhere
outside the domain. It is shown that this notion is stable under domination of
quadratic forms. As applications measure perturbations of quasi-regular
Dirichlet forms, Cheeger energies on metric measure spaces and Schr\"odinger
operators on manifolds are studied. Along the way a characterization of the
Sobolev space with Dirichlet boundary conditions on domains in infinitesimally
Riemannian metric measure spaces is obtained.
