Characterization of rectifiability via Lusin type approximation

Andrea Marchese, Andrea Merlo

We prove that a Radon measure $\mu$ on ${\mathbb{R}}^n$ can be written as $\mu ={\sum }_{i=0}^n{\mu }_i$, where each of the ${\mu }_i$ is an $i$-dimensional rectifiable measure if and only if for ever…