  Kernel-based methods provide flexible and accurate algorithms for the
reconstruction of functions from meshless samples. A major question in the use
of such methods is the influence of the samples locations on the behavior of
the approximation, and feasible optimal strategies are not known for general
problems.
  Nevertheless, efficient and greedy point-selection strategies are known. This
paper gives a proof of the convergence rate of the data-independent
\textit{$P$-greedy} algorithm, based on the application of the convergence
theory for greedy algorithms in reduced basis methods. The resulting rate of
convergence is shown to be near-optimal in the case of kernels generating
Sobolev spaces.
  As a consequence, this convergence rate proves that, for kernels of Sobolev
spaces, the points selected by the algorithm are asymptotically uniformly
distributed, as conjectured in the paper where the algorithm has been
introduced.
