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Characterization of
rectifiability via Lusin-type approximation
Andrea Marchese and Andrea Merlo |
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Vol. 17 (2024), No. 6, 2109–2121
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Abstract |
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We prove that a Radon measure on can be written as , where each of the is an -dimensional rectifiable measure if and only if, for every Lipschitz function and every , there exists a function of class such that . |
Keywords
Lipschitz functions, differentiability, Lusin-type
approximation
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Mathematical Subject Classification
Primary: 26A27, 26B05
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Milestones
Received: 3 February 2022
Revised: 15 November 2022
Accepted: 21 December 2022
Published: 19 July 2024
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Authors |
| Andrea Marchese | |
| Dipartimento di Matematica University of Trento Povo Italy |
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| Andrea Merlo | |
| Departamento de Matemáticas Universidad del País Vasco Leioa Spain |
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| © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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