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- Title
Lusin type theorems for Radon measures.
- Authors
MARCHESE, ANDREA
- Abstract
We add to the literature the following observation. If is a singular measure on Rn which assigns measure zero to every porous set and f WRn ! R is a Lipschitz function which is non-difierentiable -a.e. then for every C1 function gWRn ! R it holds {x 2 RnW f .(x) D g.(x)} D 0: In other words the Lusin type approximation property of Lipschitz functions with C1 functions does not hold with respect to a general Radon measure.
- Subjects
APPROXIMATION theory; MATHEMATICS theorems; RADON integrals; LIPSCHITZ spaces; SET theory
- Publication
Rendiconti del Seminario Matematico della Universita di Padova, 2017, Vol 138, Issue 2, p193
- ISSN
0041-8994
- Publication type
Article
- DOI
10.4171/RSMUP/138-9