Before revision:  In general, our analysis does not need any additional assumptions and also includes the case of kernels on non-compact domains. However, under the mild additional assumption of separability we observe improved rates of convergence  .
After revision:  In general, our analysis does not need any additional assumptions and also includes the case of non-Mercer kernels and also non-separable RKHS. The fail probability is controlled and decays polynomially in n, the number of samples. Under the mild additional assumption of separability we observe improved rates of convergence .