A note on the completeness of Fourier-based metrics on measures
arXiv:2402.03983
Abstract
Resolving an open question of J. A. Carillo and G. Toscani, M. Stawiska recently proved that certain metric spaces of probability measures equipped with Fourier-based metrics are complete. In this note, we extend such Fourier-based metrics to the class of complex Borel measures and consider the question of completeness in this broader setting.