A note on the completeness of Fourier-based metrics on measures

2024/02/06 by Evan Randles, Randles, Evan
Mathematics · Physics and Astronomy · #46E27 #60B10. Secondary: 42B10 #Advanced Differential Geometry Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Primary: 28A33

paper · pdf · doi:10.48550/arxiv.2402.03983

openalex publication_date 2024/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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