If I have a probability density function on $\mathbb{R}^n$. I can sample $m$ points from it. Is there anyway to get an estimate of how much probability mass is covered by balls of radius $\delta$ around each of the $m$ points?
My intuition is that if the balls intersect then I should be able to say that the distribution is somewhat concentrated and w.h.p I have covered some mass? But are there any formal results stating something like this?
What can be some very mild assumptions that can allow me to do something like this?
