Originally Posted by

**miccoli** I have a problem, that I can't do.

Let be $\displaystyle E$ a Lebesgue-measurable set of $\displaystyle R^n$, and let be $\displaystyle 0$ a point of density (of Lebesgue) for $\displaystyle E$, i.e., for all set Lebesgue-measurable $\displaystyle B$ which contains $\displaystyle 0$, we have

$\displaystyle \lim_{B\to0}\frac{|E\cap B|}{|B|}=1.$

Let be a sequence $\displaystyle {x_k}\rightarrow0$. Proof that

$\displaystyle \lim_{k\to\infty}\frac{D(x_k)}{||x_k||}=0,$

where $\displaystyle D(y)$ is the distance of $\displaystyle y$ from the set $\displaystyle E$.

Can someone help me? Thanks

($\displaystyle |\cdot|$ denote the measure of Lebesgue.)