Before revision: Given a point set P\subset R^d,  kernel density estimation for Gaussian kernel is defined as \mathcal{G}_P(x) = 1{\P\}p\in Pe^{-\left\lVert x-p \right\rVert^2} for any x\inR^d.
After revision: Given a point set P\subset R^d, a kernel density estimation for Gaussian kernel is defined as \mathcal{G}_P(x) = 1{\P\}p\in Pe^{-\left\lVert x-p \right\rVert^2} for any x\inR^d.