Criterion for the absolute continuity of curves in metric spaces

2024/06/13 by V. I. Bakhtin, Bakhtin, V. I.
Engineering · Mathematics · #51F30 #53C23 #Advanced Numerical Analysis Techniques #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2406.08941

openalex publication_date 2024/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is proved that a parameterized curve in a metric space X is absolutely continuous if and only if its composition with any Lipschitz function on X is absolutely continuous.

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