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.File in questo prodotto:
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