Abstract
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.