An important current topic in nonsmooth general relativity is to find a good notion of convergence of Lorentzian spaces. While recent works have introduced promising analogues to Gromov-Hausdorff convergence, in this talk we concentrate on its measured counterpart. We first prove a Lorentzian Gromov reconstruction theorem, which indicates a good notion of isomorphy of measured Lorentzian spaces. Based on that, we propose different definitions of measured Lorentz-Gromov-Hausdorff convergence. Finally, we outline their mutual relation as well as possible applications. In collaboration with Clemens Sämann (University of Oxford).