Let $\Phi:\Omega\times\Omega\to\Bbb R$, with $\Omega\subseteq \Bbb R^d$. We say that $\Phi$ is positive definite if for every finite set $\{ x_1, x_2,\dots, x_n\}\subset\Omega$ of distinct points the $n\times n$ matrix $A$ whose entries $A_{ij}$ are defined as $$ A_{ij} = \Phi(x_j,x_k) $$ is positive definite.
I've seen only example of positive definite functions which are also continuous. Is there any positive definite function which is not continuous?
