Lusin type theorems for Radon measures
نویسنده
چکیده
We add to the literature the following observation. If μ is a singular measure on R which assigns measure zero to every porous set and f : R → R is a Lipschitz function which is non-differentiable μ-a.e., then for every C function g : R → R it holds μ{x ∈ Rn : f(x) = g(x)} = 0. In other words the Lusin type approximation property of Lipschitz functions with C functions does not hold with respect to a general Radon measure. Mathematics Subject Classification (2010). 26A16, 41A30.
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تاریخ انتشار 2016