  Error estimates for kernel interpolation in Reproducing Kernel Hilbert Spaces
(RKHS) usually assume quite restrictive properties on the shape of the domain,
especially in the case of infinitely smooth kernels like the popular Gaussian
kernel.
  In this paper we leverage an analysis of greedy kernel algorithms to prove
that it is possible to obtain convergence results (in the number of
interpolation points) for kernel interpolation for arbitrary domains $\Omega
\subset \mathbb{R}^d$, thus allowing for non-Lipschitz domains including e.g.
cusps and irregular boundaries. Especially we show that, when going to a
smaller domain $\tilde{\Omega} \subset \Omega \subset \mathbb{R}^d$, the
convergence rate does not deteriorate - i.e. the convergence rates are stable
with respect to going to a subset.
  The impact of this result is explained on the examples of kernels of finite
as well as infinite smoothness like the Gaussian kernel. A comparison to
approximation in Sobolev spaces is drawn, where the shape of the domain
$\Omega$ has an impact on the approximation properties. Numerical experiments
illustrate and confirm the experiments.
