Show that if one uses, for the construction of the kn-NNclustering scheme, only those Xi, which are contained in a data-independent rectangle [Ln, Rn] d (where Ln → −∞ and Rn → ∞ not too fast for n →...

Show that if one uses, for the construction of the kn-NNclustering scheme, only those Xi, which are contained in a data-independent rectangle [Ln, Rn] d (where Ln → −∞ and Rn → ∞ not too fast for n → ∞), then the resulting estimate is strongly universally consistent.