Talk:Density of a set

"Theorem 4 Let $\mu$ be a locally finite Radon measure on $\mathbb R^n$. If the $n$-dimensional density $\theta^n (\mu, x)$ exists for $\lambda$-a.e. $x$, then the measure $\mu$ is given by the formula (1) where $f = \theta^n (\mu, \cdot)$."

— Really? But what happens if $\mu$ is an atom at a point? --Boris Tsirelson 19:21, 3 August 2012 (CEST)

Indeed, the correct assumption is that the density must exist for $\mu$-a.e. $x$. Thanks for pointing it out. The same error appears in Theorem 5.Camillo 08:24, 4 August 2012 (CEST)