 Skorokhod J1 topology

On càdlàg paths on a compact time interval, convergence in this topology means that increasing continuous bijections of the time interval can be chosen converging uniformly to the identity, while the corresponding time-changed paths converge uniformly to the limit. At a continuous limiting path this reduces to uniform convergence. It is a standard topology for weak limits of accelerated discrete-time chains, whose paths are step functions.