Let $R=[-1,1] \times [-1,1]$, consider the set $D=${$(x,y); x^2+y^2 \leq1$}.
$\chi_{D}$ is Riemann integrable in R.
$\chi_{D}=$$ \left\lbrace \begin{array}{l} 1 \text{ if } (x,y)\in D \\ 0 \text{ if } (x,y)\notin D \\ \end{array} \right.$
I can't find the way to do this exercise. I supposed that I need to prove that this limit is $0$: $\lim_{x \to \infty}\sum_{R_{jk}} area R_{jk}=0$. But I do not know if it is ok