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Characterization of rectifiability via Lusin-type approximation

Andrea Marchese and Andrea Merlo

Vol. 17 (2024), No. 6, 2109–2121
Abstract

We prove that a Radon measure μ on n can be written as μ = i=0nμi, where each of the μi is an i-dimensional rectifiable measure if and only if, for every Lipschitz function f : n and every 𝜀 > 0, there exists a function g of class C1 such that μ({x n : g(x)f(x)}) < 𝜀.

Keywords
Lipschitz functions, differentiability, Lusin-type approximation
Mathematical Subject Classification
Primary: 26A27, 26B05
Milestones
Received: 3 February 2022
Revised: 15 November 2022
Accepted: 21 December 2022
Published: 19 July 2024
Authors
Andrea Marchese
Dipartimento di Matematica
University of Trento
Povo
Italy
Andrea Merlo
Departamento de Matemáticas
Universidad del País Vasco
Leioa
Spain

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