We add to the literature the following observation. If µ is a singular measure on ℝn which assigns measure zero to every porous set and f ℝn → ℝ is a Lipschitz function which is non-differentiable -a.e., then for every C1 function g:ℝn → ℝ it holds (Formula Presented). In other words the Lusin type approximation property of Lipschitz functions with C1 functions does not hold with respect to a general Radon measure.

Lusin type theorems for Radon measures / Marchese, Andrea. - In: RENDICONTI DEL SEMINARIO MATEMATICO DELL'UNIVERSITA' DI PADOVA. - ISSN 0041-8994. - 138:(2017), pp. 193-207. [10.4171/RSMUP/138-9]

Lusin type theorems for Radon measures

Marchese, Andrea
2017-01-01

Abstract

We add to the literature the following observation. If µ is a singular measure on ℝn which assigns measure zero to every porous set and f ℝn → ℝ is a Lipschitz function which is non-differentiable -a.e., then for every C1 function g:ℝn → ℝ it holds (Formula Presented). In other words the Lusin type approximation property of Lipschitz functions with C1 functions does not hold with respect to a general Radon measure.
2017
Marchese, Andrea
Lusin type theorems for Radon measures / Marchese, Andrea. - In: RENDICONTI DEL SEMINARIO MATEMATICO DELL'UNIVERSITA' DI PADOVA. - ISSN 0041-8994. - 138:(2017), pp. 193-207. [10.4171/RSMUP/138-9]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/265927
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