We add to the literature the following observation. If is a singular measure on which assigns measure zero to every porous set and is a Lipschitz function which is non-differentiable -a.e., then for every function it holds
In other words the Lusin type approximation property of Lipschitz functions with functions does not hold with respect to a general Radon measure.
Cite this article
Andrea Marchese, Lusin type theorems for Radon measures. Rend. Sem. Mat. Univ. Padova 138 (2017), pp. 193–207DOI 10.4171/RSMUP/138-9