I want to find the limit in $D$$'$ (${\Bbb R}$) of the following distribution : $\frac{1}{n}\sum_{p=0}^{n-1}\delta _\frac{p}{n}$.
I thought about separating the sum of the delta function, since it is $\infty$ when $p$ is equal to $0$, and $0$ with the other value of $p$.
$\frac{1}{n }(\delta _\frac{0}{n}+\sum_{p=1}^{n-1}\delta _\frac{p}{n})$ , so the first part of the sum is $0$ and the second part is $\infty$. But computing the limit of all of this will give indeterminate form.
Any idea of how to deal with this ?