Absolutely continuous functions with values in metric spaces

2005/12/14 by Jakub Duda, Duda, Jakub · 2 citations
Mathematics · #26A46 #26E20 #Advanced Banach Space Theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Equations Stability Results #Metric Geometry (math.MG) #math.CA #math.MG #msc:26A46 #msc:26E20

paper · pdf · doi:10.48550/arxiv.math/0512340

9 pages

arxiv created 2005/12/14 · openalex publication_date 2005/12/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a general theory of absolutely continuous paths with values in metric spaces using the notion of metric derivatives. Among other results, we prove analogues of the Banach-Zarecki and Vallee Poussin theorems.

Cited by

• Statistical stability for systems semi-conjugate to pre-piecewise convex or expanding maps with countably many branches
• The speed measure and absolute continuity for curves in metric spaces

Related

• Continuity in Vector Metric Spaces
• Criterion for the absolute continuity of curves in metric spaces
• Metric derived numbers and continuous metric differentiability via homeomorphisms
• Delta-epsilon functions and uniform continuity on metric spaces
• Universally uniformly continuous metric spaces