Geodesic
Lusin type theorems for Radon measures
Marchese, Andrea1
1 Universität Zürich, Switzerland
Rendiconti del Seminario Matematico della Università di Padova, Tome 138 (2017), pp. 193-207

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We add to the literature the following observation. If μ is a singular measure on ℝ n which assigns measure zero to every porous set and f:ℝ n →ℝ is a Lipschitz function which is non-differentiable μ-a.e., then for every C 1 function g:ℝ n →ℝ it holds

μ{x∈ℝ n :f(x)=g(x)}=0.
In other words the Lusin type approximation property of Lipschitz functions with C 1 functions does not hold with respect to a general Radon measure.

Publié le :
DOI : 10.4171/RSMUP/138-9
Classification : 26, 41
Mots-clés : Lusin type approximation, Lipschitz function, porous set

Marchese, Andrea 1

1 Universität Zürich, Switzerland 
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     title = {Lusin type theorems for {Radon} measures},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {193--207},
     publisher = {European Mathematical Society Publishing House},
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Marchese, Andrea. Lusin type theorems for Radon measures. Rendiconti del Seminario Matematico della Università di Padova, Tome 138 (2017), pp. 193-207. doi: 10.4171/RSMUP/138-9

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