Lusin type theorems for Radon measures.

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. [ABSTRACT FROM AUTHOR]