  We add to the literature the following observation. If $\mu$ is a singular
measure on $\mathbb{R}^n$ which assigns measure zero to every porous set and
$f:\mathbb{R}^n\rightarrow\mathbb{R}$ is a Lipschitz function which is
non-differentiable $\mu$-a.e. then for every $C^1$ function
$g:\mathbb{R}^n\rightarrow\mathbb{R}$ it holds $$\mu\{x\in\mathbb{R}^n:
f(x)=g(x)\}=0.$$ 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.
